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.
In this case, the volume of the rectangular prism is given as 36 cm^3. Since the base and height of the rectangular pyramid are congruent to the prism, the volume of the pyramid can be calculated using the formula for the volume of a pyramid, which is V = (1/3)Bh, where B is the base area and h is the height.
Since the base and height of the pyramid are congruent to the prism, the base area of the pyramid is the same as the base area of the prism. Therefore, we have:
B = lw
Now, we can substitute the values into the formula for the volume of the pyramid:
V = (1/3)(lw)h
We know that V = 36 cm^3 and h = l (since the height of the pyramid is congruent to the base), so we can rewrite the formula as:
36 = (1/3)l^2(l)
Simplify the equation:
36 = (1/3)l^3
Multiply by 3 to get rid of the fraction:
108 = l^3
Take the cube root of both sides to solve for l:
l = 3
Therefore, the base length and height of the pyramid are both 3 cm.
To find the volume of the pyramid, we substitute the values into the volume formula for a pyramid:
V = (1/3)(lw)h
V = (1/3)(3*3)(3)
V = (1/3)(9)(3)
V = 9 cm^3
So, the volume of the rectangular pyramid with base and height congruent to the prism is 9 cm^3.
A rectangular prism has a volume of 36 cm^3. if a rectangular pyramid, has a base and height congruent to the prism, what is the pyramid?
1 answer
1 answer