LIC AAO 22 Mar 2015 Paper

Question : 33 of 160

Marks: +1, -0

What is the volume of the cylinder (in cubic metre)?
(I) The sum of height and radius of the cylinder is 24m. The total surface area of the cylinder is 2112 sq. in.
(II) LCM and HCF of the numerical values of the radius and height of the cylinderare 70 and 2 respectively. The square of numerical values of the radius of the cylinder is 96 more than the square of the numerical value of the height of the cylinder.

if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
if the data in Statement II alone arc sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
if the data in Statement I alone or in Statement II alone are sufficient to answer the question.
if the data in both the Statements I and II together are not sufficient to answer the question.
if the data in both the Statements I and II together are necessary to answer the question

Validate

Solution:

From statement I, h + r = 24 metre Total surface area of the cylinder
= 2πrh +

2πr^2

⇒ 2nr (h + r) = 2112
⇒ 2 ×

{22}/7

r × 24 = 2112
⇒ r =

{2112×7}/{2×22×24}

= 14 metres
.∴ h = 24 - 14 = 10 metre
∴ Volume of cylinder =

πr^2h

({22}/7

× 14 × 14 × 10) cu metre
= 6160 cu.metre From statement II,
Radius = 2x metre and height = 2y metre where x and y are co-primes.
∴ LCM = 2xy = 70
⇒ xy = 35 = 7x5
∴ Radius = 2 x 7 = 14 metre
Height = 10 metre
because

14^2

10^2

= 196 - 100 = 96

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