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Q:

If the base of a pyramid is a square of 6cm side and its slant height is 5cm. Find its slant surface area.

A) 50 sq.cm	B) 30 sq.cm
C) 60 sq.cm	D) 40 sq.cm

Answer & Explanation Answer: C) 60 sq.cm

Explanation:

Slant surface of a pyramid=1/2 perimeter of base slantheight

=1/2 x (4 x Side of squarebase) x Slantheight

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Filed Under: Volume and Surface Area
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Q:

What is the ratio between the volumes of a cylinder and cone of the same height and of the same diameter

A) 2:1	B) 3:1
C) 4:1	D) 5:1

Answer & Explanation Answer: B) 3:1

Explanation:

Volume of cylinder / Volume of cone = 3/1

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Q:

n is an integer chosen at random from the set

{5, 7, 9, 11 }

p is chosen at random from the set

{2, 6, 10, 14, 18}

What is the probability that n + p = 23 ?

A) 0.1	B) 0.2
C) 0.25	D) 0.3

Answer & Explanation Answer: A) 0.1

Explanation:

Each of the integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs.

Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14)

This means that the probability of getting a sum of 23 is 2/20 = 1/10

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Filed Under: Quantitative Aptitude - Arithmetic Ability
Exam Prep: GRE

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:

$4 \times 3.14 \times r^{2} : 4 \times 3.14 \times {(\sqrt{r})}^{2} = 1 : 2$

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Filed Under: Volume and Surface Area
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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 = ${πr}^{2} h$ = ${πr}^{2} \times r$ = ${πr}^{3}$

Volume of one spherical ball =r/2

Volume of the spherical ball = $\frac{\frac{4}{3} {πr}^{3}}{8}$

Number of balls=Volumeof rod/volumeof one ball

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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:

$\frac{v 1}{v 2} = \frac{{(r_{1})}^{2} \times h 1}{{(r_{2})}^{2} \times h 2}$

d1 = $2 r_{1}$ and d2 = $2 r_{2}$ are diameters

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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= $\frac{1}{3} {πr}_{1}^{2} h_{1}$

v2= $\frac{1}{3} {πr}_{2}^{2} h_{2}$

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

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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:

$\frac{v 1}{v 2} = \frac{{r_{1}}^{2} H}{{r_{2}}^{2} H}$

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Filed Under: Volume and Surface Area
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