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densk [106]
3 years ago
11

The volume of a sphere is 5,000 pie m^3. What is the surface area of the sphere to the nearest square meter?

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
5 0
The correct answer is A
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A right cylinder has a radius of r inches and height of 2r inches.
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Answer:

Part a) The lateral area is 4r^{2} \pi \ in^{2}

Part b) The area of the two bases together is 2r^{2} \pi\ in^{2}

Part c) The surface area is 6r^{2} \pi\ in^{2}

Step-by-step explanation:

we know that

The surface area of a right cylinder is equal to

SA=LA+2B

where

LA is the lateral area

B is the area of the base of cylinder

we have

r=r\ in

h=2r\ in

Part a) Find the lateral area

The lateral area is equal to

LA=2\pi rh

substitute the values

LA=2\pi r(2r)

LA=4r^{2} \pi\ in^{2}

Part b) Find the area of the two bases together

The area of the  base B is equal to

B=r^{2} \pi\ in^{2}

so

the area of the two bases together is

2B=2r^{2} \pi\ in^{2}

Part c) Find the surface area of the cylinder

SA=LA+2B

we have

LA=4r^{2} \pi\ in^{2}

2B=2r^{2} \pi\ in^{2}

substitute

SA=4r^{2} \pi+2r^{2} \pi=6r^{2} \pi\ in^{2}

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