JIPMAT 2025 (QA) - Consider the following statements, which of them is/are correct? A. If the height of cylinder is doubled, the area of curved surface is doubled. B. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. C. If a hemisphere and cone have equal bases and equal heights, then the ratio of curved surface area is sqrt(2):1. | PYQs + Solutions

JIPMAT 2025

Geometry

Solids

Hard

Consider the following statements, which of them is/are correct?
A. If the height of cylinder is doubled, the area of curved surface is doubled. $\newline$ B. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. $\newline$ C. If a hemisphere and cone have equal bases and equal heights, then the ratio of curved surface area is $\sqrt{2}:1$ .

B and C only

A and C only

A and B only

A, B and C

✅ Correct Option: 3

A. If the height of cylinder is doubled, the area of curved surface is doubled.

\newline

We know, Curved Surface Area of Cylinder

= 2 \pi r h

\newline

If height doubles, i.e.

H = 2h

, Curved Surface Area of Cylinder

=2 \pi r H = 4\pi r h

\newline

Thus, statement A is true.

B. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

\newline

We know that the total surface area of a hemisphere

= 3\pi r^2

\newline

If the radius doubles, i.e.,

R = 2r

, the total surface area of hemisphere

= 3 \pi R^2 = 3 \pi (2r)^2 = 12 \pi r^2

\newline

Thus, statement B is true.

C. If a hemisphere and a cone have equal bases and heights, then the ratio of curved surface area is

\sqrt{2}:1

\newline

Let

r

be the radius of the hemisphere.

\newline

Since the cone and the hemisphere have equal bases and heights, the base and height of the cone are

r

and

\frac{r}{2}

Thus, the slant line of the cone, say

l = \sqrt{r^2 + (\frac{r}{2})^2}= \sqrt{r^2 + \frac{r^2}{4}} = \frac{\sqrt{5}r }{2}

Curved surface area of Hemisphere

=2 \pi r^2

\newline

Curved surface area of Cone

= \pi r l = \frac{\sqrt{5} \pi r^2 }{2}

Thus, the ratio of curved surface area is

4: \sqrt5

Hence, the correct option is Option 2

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