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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

Respuesta :

1. The surface area of a cone S is S= [tex] \pi r^{2}+ \pi rl[/tex], where r is the radius of the base and l is the slant height.

2. The slant height l is found as follows:

[tex]l^{2}= OC^{2}+ OB^{2}[/tex]
[tex]l^{2}= 12^{2}+ 62^{2}=144+3844=3988[/tex]

[tex]l= \sqrt{3988}=63.15[/tex]

3. 

[tex]A=\pi r^{2}+ \pi rl=3.14(12)^{2}+3.14*12*63.15 [/tex]
[tex]= 452.16+2379.492 =2831.652 ( m^{2} )[/tex]

 [tex]= 452.16+2379.492 =2831.652 ( m^{2} )[/tex]

4. The answer is C
Ver imagen eco92

Answer:

Option C - 2833 sq.m.

Step-by-step 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

[tex]S=\pi r(r+l)[/tex]

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

[tex]l=\sqrt{r^2+h^2}[/tex]

[tex]l=\sqrt{12^2+62^2}[/tex]

[tex]l=\sqrt{144+3844}[/tex]

[tex]l=\sqrt{3988}[/tex]

[tex]l=63.15[/tex]

Substitute r and l in the formula,

[tex]S=3.14\times 12(12+63.15)[/tex]

[tex]S=3.14\times 12\times 75.15[/tex]

[tex]S=2831.67[/tex]

Approximately, [tex]S=2833m^2[/tex]

Therefore, Option C is correct.

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