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The volume of the cone changes by a factor of 27

How does the volume of the cone change

From the question, we have the following parameters that can be used in our computation:

Volume of a cone

The volume of a cone is calculated using

[tex]V = \frac13\pi r^2h[/tex]

When the radius and height are both tripled, we have

R = 3r

H = 3h

So, the new volume is

[tex]V_2 = \frac13\pi R^2H[/tex]

Substitute the known values into the equation

[tex]V_2 = \frac13\pi (3r)^2 * 3h[/tex]

Evaluate

[tex]V_2 = \frac13\pi 9r^2 * 3h[/tex]

So, we have

[tex]V_2 = \frac13\pi r^2h * 27[/tex]

Recall that

[tex]V = \frac13\pi r^2h[/tex]

So, we have

[tex]V_2 = 27V[/tex]

This means that the volume of the cone changes by a factor of 27

Question

How does the volume of a cone change if its radius and height are both tripled? A. 3 B. 9 C. 27 D. 81

Answer:

The shape of the points in the scatter plot resemble an increasing exponential equation.

Step-by-step explanation:

As you can tell it increases because it is going up on the graph.

Vertical angles are formed when two lines intersect. The measure of the ∠1 when ∠1 and ​ ∠2 ​ are vertical angles is 63°.

Vertical angles are a pair of angles formed when two lines intersect each other, these angles are always opposite to each other and measure the same.

We know about the vertical angles, therefore, if the pair of angles ∠1 and ​ ∠2 ​ are vertical angles, then the measure of the two angles is equal.

Now, as it is given that the measure of the ∠2 ​is 63° and ∠1 and ​ ∠2, therefore,

∠1 =​ ∠2 = 63°

Hence, the measure of the ∠1 when ∠1 and ​ ∠2 ​ are vertical angles is 63°.

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The flat surfaces of a 3D shape are called faces.

The faces serve as the two-dimensional polygonal areas that define the boundaries of a 3D object. In geometry, for instance, a cube is a common 3D shape that has six faces, each of which is a square. Each face is bordered by edges, which are the straight lines where two faces meet, and the corners of the faces are known as vertices (or vertex in singular form).

Examining various 3D shapes, such as the tetrahedron, which has four triangular faces, and the octahedron with its eight triangular faces, provides a clearer understanding of how faces constitute the polyhedron's shape.

Answer:

Step-by-step explanation:

Given that Hannah has 11 toothpicks that are the same length

When she uses only one toothpick for each side then we see that all sides would be equal whether quadrilateral or triangle.

Hence she can make equilateral triangles, rhombuses or squares out of these 11 toothpicks

Either one equilateral triangle, and 2 rhombuses, or one equil. triangle and 2 squares or 1 equil triangle with 1 square, 1 rhombus or 2 equil triangles with one square or rhombus

Answer:

Classroom C

Step-by-step explanation:

all you do is add it then divide it by 5 and boom

The time 8:30 can be written in two other ways using words: eight thirty and half past eight.

The time 8:30 can be written in two other ways using words as follows:

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The time 8:30 can be written in words as 'Half past eight' and 'Thirty minutes past eight'. These phrases show the same time but express it in different ways.

The time 8:30 can be written in two other ways using words. One way is to say 'Half past eight'. Another way is 'Thirty minutes past eight'. These phrases encapsulate the same time but offer variation in how the time can be expressed verbally or in writing.

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Final answer:

By setting up equations based on the given information about the garden and the sidewalk around it, and then solving for the width, we find that the width of the garden is 5 feet, and its length is 10 feet.

Explanation:

Let's denote the width of the garden as w feet. Therefore, the length of the garden can be represented as w + 5 feet, since it is mentioned that the length is 5 feet longer than its width. Surrounding the garden, there is a 2-foot-wide sidewalk which affects the overall dimensions of the combined area (garden plus sidewalk). The width and length of this entire area would thus be w + 4 and w + 9 respectively, adding 2 feet on each side for the sidewalk.

To find the area of just the sidewalk, which is given as 76 square feet, we first calculate the area of the entire (garden plus sidewalk) rectangle, and then subtract the area of the garden. The equation for the area of the entire rectangle is (w + 4)(w + 9), and for the garden alone, it's w(w + 5). The difference between these areas gives us the area of the sidewalk:

(w + 4)(w + 9) - w(w + 5) = 76

Expanding and simplifying this equation gives us a quadratic equation to solve for w. Simplifying further:

w^2 + 13w + 36 - w^2 - 5w = 76

8w + 36 = 76

8w = 40

w = 5

Therefore, the width of the garden is 5 feet and the length is 10 feet (5 + 5).

A fraction is a way to describe a part of a whole. The correct option is B.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,

2 1/2

= (2×2 + 1)/2

= 5/2

= 2.5

Given that the number that is equivalent to 43/12 can be found as shown below.

43/12

= 3 ⁷/₁₂

= 3 + 7/12

= 3 + 0.58333333

= 3.58333333

[tex]= 3.58\overline3[/tex]

Hence, the correct option is B.

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