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

The volume of the pyramid, to the nearest cubic foot is:

• 19 ft3

Some key parameters to consider:

• Base and height of the pyramid
• Volume of the pyramid= 1/3*b*h

With this in mind, we can see that the length is 2.16ft

Area is 8ft^2

The angle ACB is 30 degrees

Therefore, tan30= perpendicular/base

AB= 7.03

Then to find the volume of the pyramid is:

1/3 * b * h which gives us

$19ft {}^{3}$

Therefore, the correct answer is option D

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