Question

Find the volume of a square based pyramid like you see below if the side of the base is 10 inches and the height of the the triangular face is 20 inches. Round your answer to the nearest tenth.

Answer 1

Answer:

The volume of a square based pyramid is 645.3 cubic inches.

Step-by-step explanation:

Given:

The side of the base is 10 inches and the height of the the triangular face is 20 inches.

Now, to find the volume of square based pyramid.

Base side (a) = 10 inches.

Slant Height (s) = 20 inches.

Now, to get the height of pyramid by using pythagorean theorem:

Leg 1 = $\frac{base}{2}=\frac{10}{2}=5\ inches.$

Hypotenuse = 20 inches.

So,

Hypotenuse² = (leg 1)² + (leg 2)²

$20^2=5^2+leg2^2\\400=25+leg2^2\\Subtracting\ both\ sides\ by\ 25 \ we\ get:\\375=leg2^2$

Using square root on both sides we get:

$19.36=leg2$

leg 2 = 19.36 inches.

Thus, the height of pyramid = 19.36 inches.

Now, to get the volume of square pyramid we put formula:

h = 19.36 inches.

a = 10 inches.

$Volume=a^2\frac{h}{3}$

$Volume=10^2\times \frac{19.36}{3}$

$Volume=100\times 6.453$

$Volume=645.3\ cubic\ inches.$

Hence, the volume to the nearest tenth is 645.3 cubic inches.

Therefore, the volume of a square based pyramid is 645.3 cubic inches.