SSC GD Constable 4 Feb 2025 Shift 1 Paper

Section: Elementary Mathematics

Question : 50 of 80

Marks: +1, -0

Two cones have their heights in the ratio 4 : 3 and the radii of their bases in the ratio 1 : 2. Find the ratio of their volumes.

Solution:

Volume of cone

(V)=(1 \/ 3) π r^2 h

Calculation:
Let heights be

h _1=4 k

and

h _2=3 k

Let radii be

r _1= k

and

r _2=2 k

\;V_1=(1 \/ 3) π(k)^2(4 k)

\;⇒ V_1=(1 \/ 3) π k^3 × 4

\;V_2=(1 \/ 3) π(2 k)^2(3 k)

\;⇒ V_2=(1 \/ 3) π 4 k^2 × 3 k

\;⇒ V_2=(1 \/ 3) π 4 k^3 × 3

Ratio of volumes

= V _1: V _2

\;⇒(1 \/ 3) π k^3 × 4:(1 \/ 3) π 4 k^3 × 3

\;⇒ 4 k^3: 12 k^3

\;⇒ 1: 3

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