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Q:

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

A) 125%	B) 150%
C) 175%	D) 110%

Answer & Explanation Answer: A) 125%

Explanation:

Let the edge = a cm

So increase by 50 % = a + a/2 = 3a/2

Total surface Area of original cube = $6 a^{2}$

TSA of new cube = $6 {(\frac{3 a}{2})}^{2}$ = $6 (\frac{9 a^{2}}{4})$ = $13.5 a^{2}$

Increase in area = $13.5 a^{2} - 6 a^{2}$ = $7.5 a^{2}$

$7.5 a^{2}$ Increase % = $\frac{7.5 a^{2}}{6 a^{2}} \times 100$ = 125%

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Filed Under: Volume and Surface Area

Q:

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed

A) 486	B) 586
C) 686	D) 786

Answer & Explanation Answer: A) 486

Explanation:

Volume of new cube = $(1^{3} + 6^{3} + 8^{3}) c m^{3}$ = $729 c m^{3}$

Edge of new cube = $\sqrt[3]{729}$ = 9cm

Surface area of the new cube = ( 6 x 9 x 9) sq.cm = 486 sq.cm

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Filed Under: Volume and Surface Area

Q:

A cube of edge 15 cm is immersed completely in a rectangular vessel containing water . If the dimensions of the base of vessel are 20 cm x 15 cm, find the rise in water level

A) 11.25cm	B) 11.56cm
C) 11.66cm	D) 10.86cm

Answer & Explanation Answer: A) 11.25cm

Explanation:

Increase in volume = Volume of the cube = (15 x 15 x 15) cm3.

\Rise in water level = volume/area = (15 x 15 x 15)/(20 x 15) cm = 11.25 cm.

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Filed Under: Quantitative Aptitude - Arithmetic Ability

Q:

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A) 30	B) 40
C) 10	D) 20

Answer & Explanation Answer: B) 40

Explanation:

Volume of the block = (6 x 12 x 15) cu.cm = 1080 cu.cm

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm

= 3 cm.

Volume of this cube = (3 x 3 x 3) cu.cm = 27 cu.cm

Number of cubes = $\frac{1080}{27}$ = 40.

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Filed Under: Volume and Surface Area

Q:

The surface area of a cube is 1734 sq. cm. Find its volume

A) 2334 cubic.cm	B) 3356 cubic.cm
C) 4913 cubic.cm	D) 3478 cubic.cm

Answer & Explanation Answer: C) 4913 cubic.cm

Explanation:

Let the edge of the cube bea. Then,

6 $a^{2}$ = 1734

=> a = 17 cm.

Volume = $a^{3}$ = $17^{3}$ = 4193 cu.cm

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Filed Under: Volume and Surface Area

Q:

The diagonal of a cube is $6 \sqrt{3}$ cm. Find its surface area

A) 216 sq.cm	B) 316 sq.cm
C) 416 sq.cm	D) 516 sq.cm

Answer & Explanation Answer: A) 216 sq.cm

Explanation:

Let the edge of the cube be a.

so, the diagonal a $\sqrt{3}$ = $6 \sqrt{3}$

=> a=6

Surface area = $6 a^{2}$ = 6 x 6 x 6 = 216 sq.cm

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Filed Under: Volume and Surface Area

Q:

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

A) 8.04kg	B) 8.14kg
C) 8.24kg	D) 9.04kg

Answer & Explanation Answer: A) 8.04kg

Explanation:

Volume of the metal used in the box = External Volume - Internal Volume

= [(50 x 40 x 23) - (44 x 34 x 20)] cu.cm

= 16080 cu.cm

Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.

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Filed Under: Volume and Surface Area

Q:

Water flows into a tank 200 m x 160 m through a rectangular pipe of 1.5m x 1.25 m @ 20 kmph . In what time (in minutes) will the water rise by 2 meters?

A) 92min	B) 93min
C) 95min	D) 96min

Answer & Explanation Answer: D) 96min

Explanation:

Volume required in the tank = (200 x 150 x 2) cu.m = 60000 cu.m

Length of water column flown in1 min =(20 x 1000)/60 m =1000/3 m

Volume flown per minute = 1.5 x 1.25 x (1000/3) cu.m= 625 cu.m.

Required time = (60000/625)min = 96min

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Filed Under: Volume and Surface Area

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