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MAT Exam 2022 Paper

Question : 88 of 200

Marks: +1, -0

924 \mathrm{~m}^{3}

. Its curved surface area is ____

Solution:

Concept:

For a cylinder, volume is

\pi r^2 h

and curved surface area is

2\pi r h

. The given ratio fixes the dimensions using a common variable.

Explanation:

Let the common multiplier be

x

Then diameter

= 7x

and height

= 3x

So radius

\displaystyle r = \frac{7x}{2}

and height

h = 3x

Given volume

= 924\ \mathrm{m}^3

, we write:

\pi \left(\frac{7x}{2}\right)^2 (3x) = 924

Using

\pi = \frac{22}{7}

\frac{22}{7} \times \frac{49x^2}{4} \times 3x = 924

This simplifies to

x^3 = 8

, hence

x = 2

Now radius

\displaystyle r = \frac{7 \times 2}{2} = 7\ \mathrm{m}

and height

h = 3 \times 2 = 6\ \mathrm{m}

Curved surface area

= 2\pi r h

= 2 \times \frac{22}{7} \times 7 \times 6 = 264\ \mathrm{m}^2

Answer:

264\ \mathrm{m}^2

Correct option: B.

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