8) a regular square pvamid with base edge length 12 ft and slant hoight 10 ft

Question

UpStudy AI · Accepted Answer

To find the volume of a regular square pyramid, we can use the formula:

$$ V = \frac{1}{3}Bh $$

where:
- $$ V $$ is the volume of the pyramid,
- $$ B $$ is the area of the base of the pyramid, and
- $$ h $$ is the height of the pyramid.

Given:
- Base edge length = 12 ft
- Slant height = 10 ft

First, we need to find the height of the pyramid. We can use the Pythagorean theorem to find the height:

$$ h^2 + (\frac{12}{2})^2 = 10^2 $$

Solving for $$ h $$:

$$ h^2 + 6^2 = 10^2 $$
$$ h^2 + 36 = 100 $$
$$ h^2 = 100 - 36 $$
$$ h^2 = 64 $$
$$ h = \sqrt{64} $$
$$ h = 8 \text{ ft} $$

Now, we can find the volume of the pyramid:

$$ V = \frac{1}{3}Bh $$
$$ V = \frac{1}{3}(12^2)(8) $$
$$ V = \frac{1}{3}(144)(8) $$
$$ V = \frac{1}{3}(1152) $$
$$ V = 384 \text{ ft}^3 $$

Therefore, the volume of the regular square pyramid is 384 cubic feet.
The volume of the regular square pyramid is 384 cubic feet.

Upstudy AI Solution