Question

A solid oblique pyramid has a regular pentagonal base. The base has an edge length of 2.16 ft and an area of 8 ft2. Angle ACB measures 30°.
What is the volume of the pyramid, to the nearest cubic foot?

5 ft3
9 ft3
14 ft3
19 ft3

Answer 1

Answer:

The correct option is 4.

Step-by-step explanation:

Given: The pentagonal base with edge length of 2.16 ft and area of 8 ft². Angle ACB measures 30°

In triangle ACB,

$\tan\theta=\frac{perpendicular}{base}$

$tan(30^{\circ})=\frac{AB}{BC}$

$tan(30^{\circ})=\frac{AB}{7\sqrt{3}}$

$0.58\times 7\sqrt{3}=AB$

$0.58\times 12.12=AB$

$7.03=AB$

Volume of an oblique pyramid is

$V=\frac{1}{3}\times B\times h$

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

$V=\frac{1}{3}\times 8\times 7.03$

$V=18.75$

$V\approx 19$

The volume of the pyramid to the nearest cubic foot is 19 ft³ and option 4 is correct.

Answer 2

This solid oblique pyramid has a regular pentagonal base. The base has an edge length of 2.16 ft and an area of 8 ft2, while angle ACB measures 30°. The resulting volume of the pyramid is 5ft3 using the formula volume=1/3 area of the base x height.