A rectangular prism has a width of 92 ft and a volume of 240 ft3. Find the volume of a similar prism with a width of 23 ft.

Round to the nearest tenth, if necessary.

3.8 ft3
60 ft3
15 ft3
10.4 ft3

A pyramid has a height of 5 in. and a surface area of 90 in2. Find the surface area of a similar
pyramid with a height of 10 in. Round to the nearest tenth, if necessary.

360 in.2
180 in.2
22.5 in.2
3.6 in.2

any1?

volume of 2 similar solids is proportional to the cube of their corresponding sides, so

x/240 = 23^3/92^3 = (23/92)^3 = (1/4)^3 = 1/64
64x = 240
x = 3.75

the new volume is 3.75 ft^3

If I told you that the surface area of 2 similar solids is proportional to the square of their corresponding sides, can you set it up like I just did ?
let me know what you got.

To find the volume of a similar rectangular prism, we can use the property that the ratio between the volumes of similar figures is equal to the ratio of their corresponding side lengths raised to the power of the dimension.

The volume of the first rectangular prism is 240 ft^3 and the width is 92 ft.
The width of the second similar prism is 23 ft.

We can set up a proportion to find the volume of the second prism:

(Width of Second Prism / Width of First Prism)^3 = (Volume of Second Prism / Volume of First Prism)

(23 ft / 92 ft)^3 = (Volume of Second Prism / 240 ft^3)

0.25^3 = (Volume of Second Prism / 240 ft^3)

0.015625 = (Volume of Second Prism / 240 ft^3)

Cross-multiplying, we get:

0.015625 * 240 ft^3 = Volume of Second Prism

3.75 ft^3 = Volume of Second Prism

Rounded to the nearest tenth, the volume of the second similar prism is 3.8 ft^3.
Therefore, the correct answer is 3.8 ft^3.

For the surface area of a similar pyramid, we can use the property that the ratio between the surface areas of similar figures is equal to the ratio of their corresponding side lengths squared.

The surface area of the first pyramid is 90 in^2 and the height is 5 in.
The height of the second similar pyramid is 10 in.

We can set up a proportion to find the surface area of the second pyramid:

(Height of Second Pyramid / Height of First Pyramid)^2 = (Surface Area of Second Pyramid / Surface Area of First Pyramid)

(10 in / 5 in)^2 = (Surface Area of Second Pyramid / 90 in^2)

2^2 = (Surface Area of Second Pyramid / 90 in^2)

4 = (Surface Area of Second Pyramid / 90 in^2)

Cross-multiplying, we get:

4 * 90 in^2 = Surface Area of Second Pyramid

360 in^2 = Surface Area of Second Pyramid

Rounded to the nearest tenth, the surface area of the second similar pyramid is 360 in^2.
Therefore, the correct answer is 360 in^2.

To find the volume of a similar rectangular prism with a width of 23 ft, we can use the concept of similarity.

Similar shapes have proportional side lengths, so in this case, the ratio of the widths of the two prisms is 92 ft / 23 ft = 4.

Since volume is directly proportional to the cube of the side length, we can use the ratio of the widths to find the ratio of the volumes. In this case, the ratio of the volumes would be (4^3) = 64.

Now, we can find the volume of the similar prism using the given volume of 240 ft^3.

240 ft^3 * 1/64 = 3.75 ft^3.

Rounding to the nearest tenth, the volume of the similar prism with a width of 23 ft is 3.8 ft^3.

Therefore, the correct answer is 3.8 ft^3.

Similarly, to find the surface area of a similar pyramid with a height of 10 in, we can use the concept of similarity.

Similar shapes have proportional side lengths, so in this case, the ratio of the heights of the two pyramids is 10 in / 5 in = 2.

Since surface area is directly proportional to the square of the side length, we can use the ratio of the heights to find the ratio of the surface areas. In this case, the ratio of the surface areas would be (2^2) = 4.

Now, we can find the surface area of the similar pyramid using the given surface area of 90 in^2.

90 in^2 * 1/4 = 22.5 in^2.

Rounding to the nearest tenth, the surface area of the similar pyramid with a height of 10 in is 22.5 in^2.

Therefore, the correct answer is 22.5 in^2.