Question

A regular square pyramid has base edges of length 16 and its lateral faces are inclined 30­° to the base of the pyramid. What is the (1) height of the pyramid (2) volume of the pyramid?

Answer 1

Answer:

(1) 13.86 units.

(2) 1182.72 cubic units.

Step-by-step explanation:

Please find the attachment.

We have been given that a regular square pyramid has base edges of length 16 and its lateral faces are inclined 30­° to the base of the pyramid.

(1) We can find height of pyramid using tan.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

The length of opposite side will half the length of square base.

$\frac{16}{2}=8$

$\text{tan}(30^{\circ})=\frac{8}{h}$

$h=\frac{8}{\text{tan}(30^{\circ})}$

$h=13.8564064605420367$

$h\approx 13.86$

Therefore, the height of the pyramid will be 13.86 units.

(2). We know that volume of pyramid is 1/3 the product of base area and height.

$V=\frac{1}{3}*bh$

$V=\frac{1}{3}*16*16*13.86$

$V=\frac{1}{3}*3548.16$

$V=1182.72$

Therefore, the volume of the pyramid would be 1182.72 cubic units.