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The total surface area of a solid right circular cylinder is $1540 {cm}^{2}$ . If the height is four times the radius of the base, then find the height of the cylinder.

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28 cm

30 cm

42 cm

49 cm

answer is A.

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Detailed Solution

Given,
The total surface area of cylinder

= 1540 {cm}^{2}

Suppose radius r represent the cylinder's radius.
By given condition height h=4r
Total surface area of cylinder,

= 2 π rh + 2 π r^{2}

= 2 π r (4 r) + 2 π r^{2}

= 8 π r^{2} + 2 π r^{2}

= 10 π r^{2}

Now the total surface area is 1540 square cm. thus,

10 π r^{2} = 1540

r^{2} = \frac{154}{π}

r^{2} = \frac{154}{\frac{22}{7}}

r^{2} = \frac{154 \times 7}{22}

r^{2} = 49

\Rightarrow r = 7 cm

Therefore, height

h = 4 r

h = 4 \times 7 cm

h = 28 cm

So, the value of height is 28 cm.
Correct option is 1.

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