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A conical tent made of canvas has a base that is 20 feet across and a slant height of 14 feet. To the nearest whole unit, what is the area of the canvas, including the floor? Use 3.14 for p.

A754 ft^2
B1,193 ft^2
C2,135 ft^2
D534 ft^2

Verified Answer :

JcAlmighty

The answer is A. 754 ft^2 

The area (A) of a cone with radius r and height h is:
A = π r² + π r√(h² + r²)

We have the slant height l, so we will calculate h using the formula:
l² = r² + h²
h² = l² - r²

So:
l = 14
d = 20     - diameter
r = d/2 = 20/2 = 10
h = ?
h² = l² - r²

A = π r² + π r√(h² + r²)
A = π r² + π r√(l² - r² + r²)
A = π r² + π r√l²
A = π r² + π r l
A = 3.14 10² + 3.14 10 14 = 3.14 100 + 439.6 = 314 + 439.6 = 753.6 ≈ 754

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