CTET 2 Math and Science 07 Jul 2024 Paper

Question : 59 of 150

Marks: +1, -0

The height and base radius of a right circular cylinder are 9 cm and 6 cm respectively. If the base radius becomes half and height increases by 3 cm, then which of the following describes the new volume of the cylinder?

The new volume will be thrice the original volume.
The new volume will be one-third the original volume.
The new volume will be twice the original volume.
The new volume will be half the original volume.

Validate

Solution:

The formula for the volume of a right circular cylinder is:

V=π r^2 h

, where

r

is the base radius and

h

is the height.
Original radius

(r)=6 cm

Original height

(h)=9 cm

Calculation:
Original Volume

( V _{\;\text "original "\;}) =π ×(6)^2 × 9=π × 36 × 9=324 π cm^3

New Dimensions of the Cylinder:
New radius

=6 cm \/ 2=3 cm

New height

=9 cm+3 cm=12 cm

New Volume of the Cylinder:
New Volume

( V _{\;\text "new "\;}) =π ×(3)^2 × 12=π × 9 × 12=108 π cm^3

Now, we need to compare the new volume with the original volume:
Comparing Volumes:
Original Volume

(V_{\;\text "original "\;}) =324 π cm^3

New Volume

( V _{\;\text "new "\;}) =108 π cm^3

New Volume

\/

Original Volume

=108 π \/ 324 π=1 \/ 3

Thus, the new volume is one-third of the original volume.

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