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Wewaii [24]
3 years ago
12

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?

Mathematics
1 answer:
Sedaia [141]3 years ago
8 0

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.

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