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# Ex.13.2 Q1 Surface Areas and Volumes - NCERT Maths Class 9

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## Question

The curved surface area of a right circular cylinder of height $$14\,\rm{ cm}$$ is  $$88\,\rm{cm^2}$$  . Find the diameter of the base of the cylinder.

Video Solution
Surface Areas And Volumes
Ex 13.2 | Question 1

## Text Solution

Reasoning:

Curved surface area \begin{align} = 2\pi rh \end{align}

What is Known?

Curved surface area of the cylinder and its height.

What is Unknown?

Diameter of the base of the cylinder.

Steps:

Curved surface area of a cylinder

\begin{align} = 2\pi rh = 88\,\rm{cm^2}\,\left( \rm{given} \right) \end{align}

Height of the cylinder $$=14\,\rm{ cm}$$

\begin{align}2 \times \frac{{22}}{7} \times r \times 14 &= 88\\r = \frac{{88 \times 7}}{{2 \times 22 \times 14}} &= 1\,\rm{cm}\\2 \times \rm{radius} &= \rm{diameter}\\2 \times 1 &= 2\,\rm{cm} \end{align}

The diameter of the base of the cylinder $$=$$ $$2\, \rm{cm}.$$

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