JIPMAT 2025 (QA) - A solid brass sphere of radius 21 cm is converted into a right circular cylindrical rod of length 28 cm. The ratio of total surface areas of the rod to sphere is : | PYQs + Solutions

JIPMAT 2025

Geometry

Solids

Hard

A solid brass sphere of radius 21 cm is converted into a right circular cylindrical rod of length 28 cm. The ratio of total surface areas of the rod to sphere is :

3:1

7:6

7:3

3:7

✅ Correct Option: 2

Let the radius of the cylindrical rod be

r

Volume of the sphere:

\newline

V_{\text {sphere }}=\frac{4}{3} \pi \times (21)^{3}={4} \pi \times 7 \times 21 \times 21

cu. units

Since volume is conserved:

\newline

V_{\text {cylinder }}=\pi r^{2} \times 28={4} \pi \times 7 \times 21 \times 21

r^{2}=\dfrac{4\times 7 \times 21 \times 21}{28}=441

Thus,

r=\sqrt{441}=21

\newline

Calculating the surface areas:

Surface area of the sphere:

\newline

S_{\text {sphere }}=4 \pi \times 21^{2}

Surface area of the cylinder (including the circular ends):

S_{\text {cylinder }}=2 \pi r h+2 \pi r^{2}

=2 \pi \times 21 \times 28+2 \pi \times (21)^{2}

= 42\pi(28+21)

= 42 \pi \times 49

Finding the ratio

\dfrac{S_{\text {cylinder }}}{S_{\text {sphere }}} =\dfrac{42 \pi \times 49}{4 \pi \times (21)^2}

=\dfrac{42}{4 \times 9}

=\dfrac{7}{2 \times 3}

=\dfrac{7}{6}

Therefore, the ratio of the total surface areas of the rod to the sphere is

\dfrac{7}{6}

\newline

Hence, the correct answer is Option 2.

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JIPMAT 2025 (QA) PYQs

A solid brass sphere of radius 21 cm is converted into a right circular cylindrical rod of length 28 cm. The ratio of total surface areas of the rod to sphere is :

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