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Mathematics

Find the height of a solid circular cylinder having total surface area of 660 cm2 and radius 5 cm.

Mensuration

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Answer

Total surface area = 660 cm2

⇒ 2πr(h + r) = 660

⇒πr(h+r)=6602⇒227×5(h+5)=6602⇒h+5=330×722×5⇒h+5=2310110⇒h+5=21⇒h=21−5⇒h=16 cm.\Rightarrow πr(h + r) = \dfrac{660}{2} \\[1em] \Rightarrow \dfrac{22}{7} \times 5(\text{h} + 5) = \dfrac{660}{2} \\[1em] \Rightarrow \text{h} + 5 = 330 \times \dfrac{7}{22 \times 5} \\[1em] \Rightarrow \text{h} + 5 = \dfrac{2310}{110} \\[1em] \Rightarrow \text{h} + 5 = 21 \\[1em] \Rightarrow \text{h} = 21 - 5 \\[1em] \Rightarrow \text{h} = 16 \text{ cm.}

Hence, the height of a solid circular cylinder is 16 cm.

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