Question

38. What is the surface area of a conical grain storage tank that has a height of 62 meters and a diameter of 24 meters? Round the answer to the nearest square meter.

A) 2,381 m^2
B) 2,790 m^2
C) 2,833 m^2
D) 6,571 m^2

Answer 1

Option C - 2833 sq.m.

Explanation:

Given : A conical grain storage tank that has a height of 62 meters and a diameter of 24 meters.

To find : What is the surface area of a conical grain storage tank?

Solution :

The formula of surface area of a conical grain storage tank is

`S=\pi r(r+l)`

Where, r is the radius and l is the slant height.

Height of conical tank = 62 m

Diameter of conical tank = 24 m

Radius of conical tank = 12 m

The slant height is

`l=√(r^2+h^2)`

`l=√(12^2+62^2)`

`l=√(144+3844)`

`l=√(3988)`

`l=63.15`

Substitute r and l in the formula,

`S=3.14* 12(12+63.15)`

`S=3.14* 12* 75.15`

`S=2831.67`

Approximately,
`S=2833m^2`

Therefore, Option C is correct.

The surface area of a conical grain storage tank is 2833 sq. m.

Answer 2

1. The surface area of a cone S is S=
`\pi r^(2)+ \pi rl`, where r is the radius of the base and l is the slant height.

2. The slant height l is found as follows:


`l^(2)= OC^(2)+ OB^(2)`

`l^(2)= 12^(2)+ 62^(2)=144+3844=3988`


`l= √(3988)=63.15`

3.


`A=\pi r^(2)+ \pi rl=3.14(12)^(2)+3.14*12*63.15`

`= 452.16+2379.492 =2831.652 ( m^(2) )`


`= 452.16+2379.492 =2831.652 ( m^(2) )`

4. The answer is C