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

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.

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

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.

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