CAT Exam Model Paper 1 with solutions for free online practice

Question : 92 of 100

Marks: +1, -0

There are two cylindrical containers o f equal capacity and equal dimensions. If the radius of one of the container is increased by 12 ft and the height of another container is increased by 12 ft, then the capacity of both the container is equally increased by K cubic ft. If the actual heights of each of the container be 4 ft, then find the increased volume of each of the container:

1680 π cu ft
2304 π cu ft
1480 π cu ft
can’t be determined

Validate

Solution:

(b) Let the initial radius be r and volume be V, then

V = π r ^ { 2 } × 4

Ist case:

V _ { 1 } = π ( r + 12 ) ^ { 2 } × 4

IInd case:

V _ { 2 } = π r ^ { 2 } × ( 4 + 12 )

But

V _ { 1 } = V + K

and

V _ { 2 } = V + K

⇒V _ { 1 } = V _ { 2 }

⇒ π( r + 12 ) ^ { 2 }×4 =π r ^ { 2 } ( 16 )

r = 12 \f t

∴ Increased volume =

= V _ { 1 } = V _ { 2 } = π× ( 24 ) ^ { 2 } × 4

= 2304 π

cubic

{\ft }

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