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Q:

There is a cylinder circumscribing the hemisphere such that their bases are common. Find the ratio of their volumes

A) 3/2 B) 5/2
C) 7/2 D) 9/2
 
Answer & Explanation Answer: A) 3/2

Explanation:

R =OA = OB = Radius of hemisphere.
= Radius of cylinder ABCD.
Height of the cylinder = BC = radius

 

Volume of cylinder/Volume of hemisphere = πr323πr3

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Q:

Find the ratio of the surfaces of the inscribed and circumscribed spheres about a cube.

A) 1:2 B) 1;3
C) 1:4 D) 1:5
 
Answer & Explanation Answer: A) 1:2

Explanation:

 4×3.14×r2 : 4×3.14×r2 = 1 : 2  

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7 5090
Q:

A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod. Find the number of balls.

A) 3 B) 4
C) 5 D) 6
 
Answer & Explanation Answer: D) 6

Explanation:

Volume of rod = πr2h = πr2×r = πr3  

Volume of one spherical ball =r/2 

Volume of the spherical ball = 43πr38  

Number of balls=Volumeof rod/volumeof one ball

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7 5545
Q:

Two cylindrical buckets have their diameters in the ratio 3:1 and their heights are as 1: 3. Find the ratio of their volumes.

A) 2:1 B) 3:1
C) 4:1 D) 5:1
 
Answer & Explanation Answer: B) 3:1

Explanation:

v1v2=r12×h1r22×h2 

 

d1 = 2r1 and d2 = 2r2 are diameters

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2 2997
Q:

If the radius of base and height of a cone are increased by 10%, find the percentage of increase of its volume

A) 33.5% B) 33.1%
C) 32.1% D) 53.1%
 
Answer & Explanation Answer: B) 33.1%

Explanation:

v1= 13πr12h1

 

v2=13πr22h2

 

% Increase in volume = (V2-V1) / (V2*100)

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8 4964
Q:

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

A) 3:1 B) 2:1
C) 4:1 D) 5:1
 
Answer & Explanation Answer: A) 3:1

Explanation:

v1v2=r12Hr22H

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26 11349
Q:

What is the true discount on a bill of Rs.2916 due in 3 years hence at 8% C.I.?

A) Rs.600 B) Rs.601
C) Rs.602 D) Rs.603
 
Answer & Explanation Answer: C) Rs.602

Explanation:

PW = Amount1+R100T 

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23 3193
Q:

The present value of a bill due at the end of 2 years is Rs.1250. If the bill were due at the end of 2 years and 11 months, its present worth would be Rs.1200. Find the rate of interest and the sum.

A) rs.1175 B) rs.1375
C) rs.1475 D) rs.1575
 
Answer & Explanation Answer: B) rs.1375

Explanation:

PW = 100×Amount100+R×T 

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