Question

The total surface area of the closed cylinder is same as the surface area of the sphere. If

the height of the cylinder and the radius of the sphere is 10 cm, find the radius of the

cylinder.​

Answer 1

Here given that T.S.A of the close cylinder=S.A of sphere

and radius of sphere= height of the close cylinder

so, radius of sphere and height of the close cylinder is 10 cm

S.A of sphere=4πr² and T.S.A of cylinder= 2πr(r+h)

now we find S.A of sphere=4πr²

4×22/7×10×10

=8800/7

therefore T.S.A of cylinder=2πr(r+h)=8800/7

=2×22/7r(r+10)=8800/7

=44/7×r(r+10)=8800/7

=44/7×r²+10r=8800/7

r²+10r=8800/7÷44/7

r²+10r=8800/7×7/44

r²+10r=8800/44

r²+10r=200

r²+10r-200=0

r²-10r+20r-200

r(r-10)20(r-10)

(r-10)(r+20)=r=10 and -20

therefore r=10 becaus radius can not be negative

radius of the cylinder =10 cm