To determine: Find the lateral area of the conical tent.

Question

i1ziZ · Accepted Answer

The lateral area of the conical tent is

Accepted Answer

Step 1

Formula used: The lateral area L of cone with radius r of base is

$L = \frac{1}{2} P l = \frac{1}{2} 2 π r l = π r l$ , where 1 is the slant height and P is the perimeter of the base

Calculation:

diameter=13 ft

radius $= r = \frac{13}{2} = 6.5$ ft inches

Use Pythagoras Theorem to find the slant height of the cone $= 1 = \sqrt{{6.5}^{2} + 8^{2}} \approx 10.31 f t$

Lateral area of the conical tent $= L = π r l = π (6.5) (10.31) \approx 210.5 f t^{2}$

Step 2

Formula used: The surface area of a cone:

S+L+B, where L is the lateral area of the cone and B is the area of the base.

Calculation:

From part(1), Lateral area $= L = 210.5 f t^{2} a n d t h e r a d i u s = r = 6.5 f t$

the area of the base $= B = π r^{2} = π (6.5)^{2} = 132.73 f t^{2}$

Surface area of the conical tent $= S = L + B = 210.5 + 132.73 = 343.2 f t^{2}$

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