Question

find the volume, in cubic inches, of the composite solid below, which consists of a pyramid sitting on top of a cube. the pyramid has the same base as the cube. enter only the number. 10 inch 10 inch 8 inch height the solution is

Explanation:

Step1: Calculate cube volume

The volume formula for a cube is $V_{cube}=s^3$, where $s = 10$ inches. So $V_{cube}=10^3=1000$ cubic - inches.

Step2: Calculate pyramid volume

The base of the pyramid is a square with side - length $s = 10$ inches, so the base area $B=s^2=10^2 = 100$ square inches. The height of the pyramid $h = 8$ inches. The volume formula for a pyramid is $V_{pyramid}=\frac{1}{3}Bh$. Substituting the values, we get $V_{pyramid}=\frac{1}{3}\times100\times8=\frac{800}{3}$ cubic inches.

Step3: Calculate composite - solid volume

The volume of the composite solid $V = V_{cube}+V_{pyramid}$. So $V=1000+\frac{800}{3}=\frac{3000 + 800}{3}=\frac{3800}{3}\approx1266.67$ cubic inches.

Answer:

$\frac{3800}{3}$