Volume and Surface Areas Quiz Set 010

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Question 1

What is the length of an edge of a cube if the ratio of volume to the total surface area is 41 : 23?

 A

$10{16/23}$ units.

 B

$12{5/22}$ units.

 C

$8{23/25}$ units.

 D

$12{3/5}$ units.

Soln.
Ans: a

The well-known relation for a cube is $S/V = 6/a$, which can be re-arranged to get $a = 6 × V/S$ = ${246/23}$, which is same as: $10{16/23}$.


Question 2

A room has a floor size of 17 × 43 sq. m. What is the height of the room if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls?

 A

$12{11/60}$ m.

 B

$13{24/59}$ m.

 C

$10{51/62}$ m.

 D

$14{43/62}$ m.

Soln.
Ans: a

Let h be the height, and l and b be the length and breadth. We are given lb + lb = lh + hb + lh + hb. Combining the terms and cancelling 2, we get lb = h(l + b), which gives h = ${lb}/{l + b}$ = ${17 × 43}/{17 + 43}$ = ${731/60}$, which is same as: $12{11/60}$ m.


Question 3

How many boxes measuring 1 m × 1m × 1 m should be dropped into a water tank 6 m × 8 m so that the water level rises by 1 m?

 A

48 .

 B

50 .

 C

46 .

 D

52 .

Soln.
Ans: a

The volume of water to be displaced is 6 × 8 × 1 cu. m. This should be equal to the volume of the boxes to be dropped. So N × 1 × 1 × 1 = 6 × 8 × 1, which gives N = 6 × 8 = 48.


Question 4

How much water flows per hour through a pipe of radius 49 cm, if water flows at 10 km/h? Take π = 22/7.

 A

7546 cu. m.

 B

7548 cu. m.

 C

7544 cu. m.

 D

7550 cu. m.

Soln.
Ans: a

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is ${22 × 49 × 49 × 10 × 1000}/{7 × 100 × 100}$, which can easily be cancelled to get 7546 cu. m.


Question 5

The areas of three adjacent faces of a cube are 2, 3 and 6. It's volume is?

 A

6 cu. units.

 B

8 cu. units.

 C

4 cu. units.

 D

10 cu. units.

Soln.
Ans: a

Let the sides be L, B and H. Then LB = 2, BH = 3 and LH = 6. Multiplying all three of them L2B2H2 = (2 × 3 × 6) = 36 = 62, which gives LBH = 6 = volume of the cuboid.


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Creative Commons License
This Blog Post/Article "Volume and Surface Areas Quiz Set 010" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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