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?(1 point)

Responses

20 cm
20 cm

4 cm
4 cm

5 cm
5 cm

43 cm
Start Fraction 4 over 3 End Fraction cm

1 answer

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism. The volume of a pyramid is given by the formula V = 1/3 * Bh, where B is the area of the base and h is the height of the pyramid.

Given that the base area of the rectangular prism is 15 cm^2 and the volume of the pyramid is 20 cm^3, we can set up two equations based on the formulas:

1) l * w = 15
2) (1/3) * 15 * h = 20

From equation 1, we can express the length l in terms of the width w: l = 15/w

Plugging this into the second equation and solving for h:
(1/3) * 15 * h = 20
5 * h = 20
h = 4 cm

Therefore, the height of the rectangular prism is 4 cm.