Question

what is the surface area of a conical grain storage tank that has a height of 24 meters and a diameter of 16 meters? round the answer to the nearest square tenth.

Answer 1

The basis of this cone is a circle with a diameter d = 16m. This information is sufficient to calculate
1. The surface of the wheel . We use the formula


`A = \pi r^(2)`

2. the radius of the wheel needed to the formula for calculating the area of ​​a circle and the cone

d = 16m
1/2d = r = 1/2*16m = 8m
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Area base

`P = \pi r^(2) = \pi (8m)^(2) = 64 \pi m^(2)`
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The surface area


`A = \pi rl`
l - creates a cone = ?

Height , forming a cone and the radius of a circle formed triangle . Two known sides is possible to calculate the third side ( the cone ) of the Pythagorean Theorem

a = r = 8cm
b = h = 24m
c = l = ?

a² + b² = c²
r² + h² = l²
l = √ (r² + h²) = √ [ ( 8m)² + ( 24m)² ] = √ (64m² + 576m²) = √ (640 m²)= √ (8*8*10m²) = 8√10m

The lateral surface of the cone
A = πrl = π*8m *8√10m = 64√10πm²

The total area of ​​the cone = The base area of ​​the side surface of +

A = 64√10πm² + 64πm² = 64πm² *(√10 + 1)