Question

Find the surface area and volume of the pyramid. ​

Answer 1

Given:

The figure of a square base pyramid.

To find:

The area of volume of the pyramid.

Solution:

The area of square base is:

$B=(side)^2$

$B=(16)^2$

$B=256$

Area of one triangular side of the pyramid is:

$A_1=\dfrac{1}{2}\times base\times height$

$A_1=\dfrac{1}{2}\times 16\times 13$

$A_1=104$

Now, the total surface area of the pyramid is:

$A=B+4A_1$

$A=256+4(104)$

$A=256+416$

$A=672$

Therefore, the surface area of the pyramid is 672 square m.

The volume of the pyramid is:

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

Where, B is the base area and h is the vertical height of the pyramid.

Substituting $B=256,\ h=6$, we get

$V=\dfrac{1}{3}(256)(h)$

$V=(256)(2)$

$V=512$

Therefore, the volume of the pyramid is 512 cubic meters.

Hence the correct option is d.