Question

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.

A. 754 ft^2
B. 1,193 ft^2
C. 2,135 ft^2
D. 534 ft^2

Answer 1

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