Volume and Surface Areas Quiz Set 017 | Maths Aptitude Quiz Questions and Mock Test on Volume and Surface Areas Set 17 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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Question 1

A room has a floor size of 13 × 37 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?

$9{31/50}$ m.

$10{41/49}$ m.

$8{15/52}$ m.

$12{7/52}$ 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 = ${lb}/{l + b}$ = ${13 × 37}/{13 + 37}$ = ${481/50}$, which is same as: $9{31/50}$ m.

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Question 2

What is the length of an edge of a cube if the ratio of volume to the total surface area is 13 : 31?

$2{16/31}$ units.

$3{19/30}$ units.

$1{14/33}$ units.

$5{2/11}$ units.

Soln.
Ans: a

The well-known relation for a cube is $S/V = 6/a$, which can be re-arranged to get $a = 6 × V/S$ = ${78/31}$, which is same as: $2{16/31}$.

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Question 3

What is the weight of a hollow cylindrical pipe 14 cm long, and having internal and external radii as 14 and 16 cm? The pipe is made of a metal of density 6 gm/cc. Take π = 22/7.

15840 gm.

15842 gm.

15838 gm.

15844 gm.

Soln.
Ans: a

The volume of the pipe is π × (16² - 14²) × 14, which is $22/7$ × 60 × 14. Weight = vol × density = $22/7$ × 60 × 14 × 6 = 15840 gm.

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Question 4

An iron tank 2 m × 6 m is filled with water upto a height of 4 m. What surface area of the tank is at a higher risk of corrosion?

76 cu. m.

78 cu. m.

74 cu. m.

80 cu. m.

Soln.
Ans: a

If L, B and H are the dimensions of the water column, then the wet area is 2(BH + LH) + LB = 2 × (6 × 4 + 2 × 4) + 2 × 6. The result is 76 cu. m.

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Question 5

The areas of three adjacent faces of a cube are 5, 6 and 30. It's volume is?

30 cu. units.

32 cu. units.

28 cu. units.

34 cu. units.

Soln.
Ans: a

Let the sides be L, B and H. Then LB = 5, BH = 6 and LH = 30. Multiplying all three of them L²B²H² = (5 × 6 × 30) = 900 = 30², which gives LBH = 30 = volume of the cuboid.

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