Question

What is the volume of the frustum?

A. 258.47
B. 503.77
C. 588
D. 147

Answer 1

V = 1/3 πh(R^2 +r^2 + R*r)
V = 1/3 (3.14)(14) (4.2^2 + 2.5^2 + 4.2 * 2.5)
V = 1/3 (3.14)(14) (17.64 + 6.25 + 10.5)
V = 1/3 (3.14)(14) (34.39)
V = 503.93

Because i'm using π = 3.14

So answer is B. 503.77

Answer 2

The formula for the volume of a frustum of a cone is
V = (1/3)π·(R² + r² +r·R)·h
where R and r are the radii of the circular faces.

For your figure, R = 4.2, r = 2.5, h = 14. Filling in the given numbers, you have
V = (π/3)(4.2² +2.5² +4.2·2.5)·14 ≈ 504.18

It looks like the appropriate choice is probably
B. 503.77


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Sometimes the answers to these problems are figured using incorrect rounding and inappropriate values of π. It looks like this answer key was simply miscalculated.