There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3 , what is the volume of the prism

Answer 1

Since the prism and pyramid have congruent bases and height, the volume of the prism can be calculated using the formula for the volume of a prism, which is V = B × h, where B is the area of the base and h is the height.

Given that the volume of the pyramid is 48 in.³, we know that the volume of the pyramid is equal to one-third of the volume of the prism, as they have the same base and height. Therefore, the volume of the prism can be calculated as follows:

Volume of prism = 3 × Volume of pyramid
Volume of prism = 3 × 48 in.³
Volume of prism = 144 in.³

Therefore, the volume of the rectangular prism is 144 in.³.

Answer 2

A rectangular prism has a base area of 15 cm2 , and pyramid with a congruent base and height has a volume of 20 cm3 . What is the height of the rectangular prism

Answer 3

Since the base area of the rectangular prism is 15 cm² and the volume of the pyramid with a congruent base and height is 20 cm³, we can determine the height of the rectangular prism by using the formula for the volume of a rectangular prism.

Let's first find the height of the pyramid since it is given: V_pyramid = 1/3 * B_base * h_height
20 cm³ = 1/3 * 15 cm² * h_height
20 = 5h
h_height = 4 cm

Now we can find the height of the rectangular prism using this height: V_prism = B_base * h_prism_height
20 cm³ = 15 cm² * h_prism_height
h_prism_height = 20 cm² / 15 cm²
h_prism_height = 4/3 cm
h_prism_height = 1.33 cm

Therefore, the height of the rectangular prism is 1.33 cm.

Answer 4

1. 144
2. 4
3. prism: 108; pyramid: 36
4. The volume of the prism is three times as large as the volume of the pyramid
5. 364