A piece of solid, spherical glass has a circumference of 18.84 centimeters. The sphere is cut in half, creating two identical hemispheres. Using 3.14 for π, Tran computes the amount of paint needed to cover the sphere. Which statement about the amount of paint found by Tran is true?
Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere
Tran found the minimum amount of paint needed to cover the entire surface of one of the hemispheres.
Tran found the minimum amount of paint needed to cover both hemispheres.
Tran found the minimum amount of paint needed to cover the bases of both hemispheres.
Final answer:
Tran must calculate the surface area of the hemisphere, including the base, to determine the amount of paint needed, which is the sum of half the surface area of the sphere and the area of the base.
Explanation:
The question is asking what Tran would compute when using π to determine the amount of paint required for a hemisphere. First, Tran needs to calculate the surface area of the sphere to determine the paint needed. Given the circumference C = 18.84 cm, the radius r can be found using C = 2πr, which gives us a radius of r = C / (2π). Once we have the radius, we can find the surface area A of the sphere using A = 4πr², which is necessary to determine the paint needed for the outer surface.
However, when the sphere is cut into two hemispheres, the flat face of each hemisphere (base) also needs paint. The area of the base is a circle with an area of πr². Thus, the total surface area that Tran would need to paint for one hemisphere, including the base, is πr² + 2πr² (half of the sphere's surface area).
Final answer:
Option D.) Tran found the minimum amount of paint needed to cover both hemispheres.
Explanation:
Tran found the minimum amount of paint needed to cover both hemispheres. To calculate the amount of paint needed to cover a hemisphere, we need to find the surface area of the hemisphere. The formula for the surface area of a sphere is 4πr², where r is the radius.
Given that the circumference of the sphere is 18.84 centimeters, we can use the formula C = 2πr to solve for the radius. Plugging in the value for C, we get 18.84 = 2πr.
Simplifying the equation, we find that the radius of the sphere is approximately 3 centimeters.
The surface area of a hemisphere is half the surface area of a sphere, so the surface area of one hemisphere is 2πr²/2 = πr².
Substituting the value of r, we find that the surface area of one hemisphere is approximately 9π square centimeters.
Since Tran cut the sphere in half and created two identical hemispheres, the minimum amount of paint needed to cover both hemispheres would be twice the surface area of one hemisphere, which is approximately 18π square centimeters.
a 5 inch tall bamboo shoot doubles in height every 3 days. if the equation, y=ab^x where x is the number of doubling periods, represents the height of the bamboo shot, what are the values of a and b?
round 149,640 to the nearest thousand.
A thermometer is removed from a room where the temperature is 70° f and is taken outside, where the air temperature is 30° f. after one-half minute the thermometer reads 50° f. what is the reading of the thermometer at t = 1 min? (round your answer to two decimal places.)
In a circle with a radius of 27 2/5 in., an arc is intercepted by a central angle of 7π/4 radians. What is the arc length? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
For future reference, Scapazzi was correct.
The arc length will be given as the circumference of the circle is 150.56 inches long.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
In a circle with a radius of 27 + 2/5 inches.
That can be written as 27.4.
An arc is intercepted by a central angle of 7π/4 radians.
The arc length will be given as the circumference of the circle
[tex]\rm Arc \ length = \dfrac{\theta}{2\pi} 2 \pi*r\\\\Arc \ length = \theta * r\\\\Arc \ length = \dfrac{7 \pi }{4} * 27.4 \\\\Arc \ length = 150.56[/tex]
Thus, the arc length will be given as the circumference of the circle is 150.56 inches.
More about the circle link is given below.
https://brainly.com/question/11833983
if i have 2 c's 2 A's 3 b's and 1 d what is my gpa and would i be able to pass 8th grade
Find the domain and range of the relation and determine whether it is a function.
a. domain: all real numbers; range: all real numbers; Yes, it is a function.
b. domain: positive integers; range: positive integers; No, it is not a function.
c. domain: x ≥ 0; range: y > 3; No, it is not a function.
d. domain: x > 3; range: y > 0; Yes, it is a function.
Using function concepts, it is found that the correct option is:
d. domain: x > 3; range: y > 0; Yes, it is a function.
A relation is a function if for each value of the input, there is only one respective value of the output. In a graph, it means that for each value of x, there is only one respective value of y.
In this graph, there is only one value of y for each value of x, hence, it is a function.The domain of a function is the set that contains all possible input values. In a graph, it is the values assumed by x, the horizontal axis.
In this graph, x assumes values greater than 3, hence the domain is x > 3.The range of a function is the set that contains all possible output values. In a graph, it is the values assumed by y, the vertical axis.
In this graph, y assumes values greater than 0, hence the range is y > 0.A similar problem is given at https://brainly.com/question/10891721
Miguel has an aquarium in the shape of a rectangular prism. The base is 30.25 inches long and 12.5 inches wide. The aquarium is 12.75 inches high. What is the volume of the aquarium to the nearest cubic inches?
The result of 4,816.40625 cubic inches is rounded to 4,816 cubic inches to the nearest cubic inch.
To find the volume of Miguel's aquarium, which is in the shape of a rectangular prism, we use the formula for the volume of a rectangular prism:
Volume = length * width * height
In this case, the length is 30.25 inches, the width is 12.5 inches, and the height is 12.75 inches.
So, the calculation for the volume would be:
Volume = 30.25 inches * 12.5 inches * 12.75 inches
= 4,816.40625 cubic inches.
Rounding to the nearest cubic inch, the volume of the aquarium is 4,816 cubic inches.
Look at this cube and its net. Cube with one side labeled 8 centimeters. Net of the same cube also shown with one side labeled 8 centimeters. What is the surface area of this cube? cm²
1.) A circle has a radius of 12 centimeters. Find the area of the sector of the circle formed by an angle of 25 degrees. is necessary, round the answer to two decimal places.
2.) Is the function f(theta) = sin theta + cos theta even, odd, or neither? show how
When p2 – 4p is subtracted from p2 + p – 6, the result is 5p-6 To get p – 9, subtract
Subtract p² - 4p from p² + p - 6 to get 5p - 6. To obtain p - 9, subtract 15 from 5p - 6.
Let's break it down step by step:
1. Subtracting p² - 4p from p² + p - 6:
Start by writing down the expression p² + p - 6.
Now, subtract p² - 4p from it term by term.
(p² + p - 6) - (p² - 4p)
2. Expand and Simplify:
Distribute the subtraction across each term inside the parentheses:
p² + p - 6 - p² + 4p
This simplifies to: (p² - p²) + (p + 4p) - 6
= 0 + 5p - 6
= 5p - 6
3. Now, to get p - 9:
We want to manipulate 5p - 6 to p - 9.
Subtracting 15 from 5p - 6 gives:
5p - 6 - 15
= 5p - 21
Therefore, subtracting 5p - 21 from 5p - 6 results in p - 9.
Find the value of x to the nearest tenth.
10.0
6.0
9.3
4.0
Answer:
The value of x is 6
Step-by-step explanation:
Given the figure in which
DE=3x-8 and BC=20
we have to find the value of x.
By mid-point theorem which states that the line segment which is drawn to the mid-points of two sides of triangle is parallel to the third side and also half of the length of third side.
[tex]DE=\frac{1}{2}BC[/tex]
[tex](3x-8)=\frac{1}{2}\times 20[/tex]
[tex]3x-8=10[/tex]
[tex]3x=18[/tex]
[tex]x=\frac{18}{3}=6[/tex]
The value of x is 6
Option 2 is correct.
One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse? 2.5 inches 5.0 inches 7.1 inches 9.8 inches
Answer: 7.1 inches
Step-by-step explanation:
Given: One leg of isosceles right triangle = 5 inches
Since in isosceles right triangle , two sides have same side length , therefore the length of the other leg should be 5 inches.
Let H be the hypotenuse of the isosceles right triangle
Now, by Pythagoras Theorem , we have
[tex]H^2=5^2+5^2=25+25=50\\\\\Rightarrow\ H=\sqrt{50}=5\sqrt{2}\\\\\Rightarrow\ H==5\times(1.41421356237)\\\\\Rightarrow\ H==7.07106781187\approx7.1\ inches[/tex]
Hence, the approximate length of the hypotenuse = 7.1 inches
Answer: C
Step-by-step explanation: 7.1 inches
A person's website specializes in the sale of rare or unusual vegetable seeds. he sells packets of sweet-pepper seeds for $2.32 each and packets of hot-pepper seeds for $4.40 each. he also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $2.58 per packet. how many packets of each type of seed are in the assortment?
Suppose you toss a coin 100 times and get 69 heads and 31 tails. based on these results, what is the probability that the next flip results in a tail?
The distance from town A to town B is divided into 8 equal parts. So far, a bus has traveled 12 Miles. How far apart are town A and town B? Explain
Town A and Town B are 1.5 miles apart.
Explanation:The distance between town A and town B can be found by multiplying the distance traveled by the number of equal parts that make up the whole distance. In this case, the bus has traveled 12 miles out of 8 equal parts. To find the total distance, we can set up a proportion:
12 miles / 8 parts = x miles / 1 part
Cross-multiplying gives us:
8x = 12 miles
Dividing both sides by 8 gives us:
x = 1.5 miles
Therefore, town A and town B are 1.5 miles apart.
Help please!!! Need to find the height!!
The measure of DF is 108. What is the measure of DEF, the tangent-chord angle?
Answer:
The measure of DE is 108°. What is the measure of ZDEF, the tangent-chord angle?
54
Step-by-step explanation:
For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 7 3 π meters?
Answer : The measurement of a central angle is, [tex]140^o[/tex]
Step-by-step explanation :
Formula used for angle subtended by an arc is:
[tex]s=\frac{\pi r\theta}{180}[/tex]
where,
s = arc length = [tex]\frac{7}{3}\pi m[/tex]
r = radius = [tex]\frac{diameter}{2}=\frac{6m}{2}=3m[/tex]
Now put all the given values in the above formula, we get:
[tex]s=\frac{\pi r\theta}{180}[/tex]
[tex]\frac{7}{3}\pi=\frac{\pi \times (3)\times \theta}{180}[/tex]
[tex]\theta =140^o[/tex]
Thus, the measurement of a central angle is, [tex]140^o[/tex]
One side of a triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. if the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 21 cm long, the second side is 36 cm, and the angle is π/6? (round your answer to three decimal places.)
The rate at which the angle between the sides of the triangle is changing is 4/9 radians per second.
Explanation:In this problem, we are given that one side of the triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. We need to find the rate at which the angle between the sides is changing.
To solve this, we can use the formula:
angle_rate = (-side2_rate/side1)*(cos(angle))/(sin(angle))
Substituting the given values:
angle_rate = (-(-2)/9)*(cos(π/6))/(sin(π/6))
Simplifying, we get:
angle_rate = 4/9
Therefore, the rate at which the angle between the sides is changing is 4/9 radians per second.
Learn more about Rate of change here:https://brainly.com/question/31226174
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Roselyn wants to drive her car at a speed of 60 miles per hour for 1.251, point, 25 hours. Her car has a fuel efficiency of 15 miles per gallon. How many gallons of fuel does Roselyn need for her journey? Choose 1 answer: Choose 1 answer: A 2.52, point, 5 gallons B 3.1.25, point, 125 gallons C 0.20, point, 2 gallons D 5 gallons
The number of gallons of fuel Roselyn need for her journey is:
D. 5 gallons
Step-by-step explanation:It is given that:
Roselyn wants to drive her car at a speed of 60 miles per hour for 1.25 hours.
This means that the total distance she covers in 1.25 hours is:
[tex]60\times 1.25=75\ \text{miles}[/tex]
( Since, we know that speed is defined as the ratio of distance to time.
i.e.
[tex]Speed=\dfrac{Distance}{Time}\\\\i.e.\\\\Distance=Speed\times Time[/tex] )
Also, Her car has a fuel efficiency of 15 miles per gallon.
i.e.
She could cover 15 miles with 1 gallon of fuel.
Hence, in order to cover 75 miles.
i.e. to cover (15×5) miles she needs (1×5) gallons of fuel
i.e. she needs 5 gallons of fuel to cover 75 miles.
708,000 divided by 3,000 equals
How to find the volume of a hemispherical bowl depth h?
There are 24 different tables to set up for field day.The principal wants the tables set up in equal rows.should she use 3 rows or 5 rows?Explain
does 6% of a pound weigh more than an ounce
Answer:
6% of a pound does not weigh more than 1 ounce.
Step-by-step explanation:
First, we will calculate 6% (0.06) of 1 pound.
0.06 × 1 lb = 0.06 lb
1 pound is equal to 16 ounces. 0.06 pounds, expressed in ounces is:
0.06 lb × (16 oz/ 1 lb) = 0.96 oz
6% of a pound = 0.96 oz
0.96 oz < 1 oz
Due to the transitive property, we can affirm that 6% of a pound does not weigh more than 1 ounce.
what is −1.6+(−2.4)?
NEED ANSWER IN LEAST THAN 3 Minutes
Anita owns a beauty supply store. Every two weeks she receives a supply of shampoo. Every four weeks she receives a carton of nail polishes. Every eight weeks she receives a box of combs, and every twelve weeks she receives a box of hair dyes. If Anita received a shipment of all these supplies today, when is the next time all four supplies will arrive on the same day?
least common denominator for 1/49 1/21 1/3
what is the volume of a box that can fit exactly 128 1/8 inch cubes with 1/2 inch sides?
A computer and printer cost a total of 1136
. The cost of the computer is three times the cost of the printer. Find the cost of each item.