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MCQ Questions on Mensuration 3D for Competitive Exams

Ace your competitive exams with our MCQ questions on Mensuration 3D. Learn to solve volume and surface area problems with questions designed to test your knowledge effectively. Page-4 section-1

Each section contains 100 MCQs on Mensuration 3D .
31
The height of a solid cylinder in 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm2) of the remaining solid?
Discuss
Answer & Solution
Answer: Option A
Solution:
Mensuration 3D mcq question image
L.S.A. of cylinder = 2πrh
= 2 × $$\frac{{22}}{7}$$ × 5 × 30
= 300π
L.S.A. of cones = 2[πr$$l$$]
= 2[π × 5 × 13]
= 130π
T.S.A. of remaining part
= 300π + 130π
= 430π
32
The internal measure of a cuboidal room are with length as 12 m, breadth as 8 m and height as 10 m. The total cost (in Rs.) of white washing all four walls of the room and also the ceiling of the room, if the cost of white washing is Rs. 25 per m2 is:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$l$$ = 12 cm
b = 8 cm
h = 10 cm
Cost = Rs. 25/m2
Area of 4 walls = 2($$l$$ + b) × h
= 2(12 + 8) × 10
= 400 m2
Area of roof = 12 × 8 = 96 m2
Total Area = 400 + 96 = 496
Cost = 496 × 25 = Rs. 12400
33
If the radius of a sphere is increased by 4 cm, its surface area is increased by 464π cm2. What is the volume (in cm3) of the original sphere?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & 4\pi \left[ {{{\left( {R + 4} \right)}^2} - {R^2}} \right] = 464\pi \cr & 4\left( {R + 4 + R} \right)\left( {R + 4 - R} \right) = 464 \cr & 16\left( {2R + 4} \right) = 464 \cr & 2R + 4 = 29 \cr & R = \frac{{25}}{2} \cr & {\text{Volume of sphare}} = \frac{4}{3}\pi {R^3} \cr & = \frac{4}{3}\pi \times {\left( {\frac{{25}}{2}} \right)^3} \cr & = \frac{4}{3} \times \frac{{15625}}{8}\pi \cr & = \frac{{15625}}{6}\pi \cr} $$
34
Which of the following two will provide more volume?
I. A cuboid of edges 6 cm, 7 cm and 8 cm
II. A cube of edge 7 cm
Discuss
Answer & Solution
Answer: Option A
Solution:
(I) 6 × 7 × 8 = 336
(II) (7)3 = 343
Cube will have more volume.
35
The curved surface area of a right circular cone is 2310 cm2 and its radius is 21 cm. If its radius is increased by 100% and height is reduced by 50%, then its capacity (in litres) will be (correct to one decimal place): $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Curved surface area of cone}} = \pi rl \cr & \frac{{22}}{7} \times 21 \times l = 2310 \cr & 66l = 2310 \cr & l = 35 \cr & {\text{Height}} = \sqrt {{{35}^2} - {{21}^2}} \cr & = \sqrt {1225 - 441} \cr & = \sqrt {784} \cr & = 28{\text{ cm}} \cr & {\text{New radius}} = 21 + 21 = 42{\text{ cm}} \cr & {\text{New height}} = 28 - 14 = 14{\text{ cm}} \cr & {\text{New volume}} = \frac{1}{3}\pi {r^2}h \cr & = \frac{1}{3} \times \frac{{22}}{7} \times 42 \times 42 \times 14 \cr & = 22 \times 42 \times 28 \cr & = 25872{\text{ c}}{{\text{m}}^3} \cr & {\text{Capacity}} = \frac{{25872}}{{1000}} = 25.9{\text{ litres}} \cr} $$
36
A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?
Discuss
Answer & Solution
Answer: Option A
Solution:
Total surface area = perimeter × height + 2 × area of base
216√3 = 6 × 6 × h + 2 × 6 × $$\frac{{\sqrt 3 }}{4}$$ × 6 × 6
216√3 = 36h + 108√3
108√3 = 36h
h = 3√3 cm
37
Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long 44 m wide. The time taken (in hours) for the rise in the level of water in the tank to be 7 cm is
Discuss
Answer & Solution
Answer: Option A
Solution:
Let the time taken to fill the tank = $$x$$ hours
$$\eqalign{ & \Rightarrow \left( {\pi {r^2}h} \right) \times x = 50 \times 44 \times \frac{7}{{100}} \cr & \Rightarrow x = \frac{{50 \times 44 \times 7 \times 7 \times 100 \times 100}}{{22 \times 7 \times 7 \times 100 \times 5000}} \cr & \Rightarrow x = 2{\text{ hours}} \cr} $$
38
The areas of three adjacent faces of a cuboidal tank are 3 m2, 12 m2 and 16 m2. The capacity of the tank, in litres is:
Discuss
Answer & Solution
Answer: Option C
Solution:
Note 1 m3 = 1000 litres
1000 cm3 = 1 litre
V2 = abc
V = $$\sqrt {3 \times 12 \times 16} $$
V = 6 × 4 = 24m3 = 24000 litres
39
If a cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes?
Discuss
Answer & Solution
Answer: Option D
Solution:
Volume of cuboid = 32 × 12 × 9
Volume of a cube = 16 × 12 × 9
a3 = 16 × 12 × 9
a = 12
Area of cuboid : Area of two cube
= 2(32 × 12 + 12 × 9 + 9 × 32) : 2 × 6 × 122
= 65 : 72
40
A sector is formed by opening out a cone of base radius 8 cm and heigh 6 cm. Then the radius of the sector is (in cm).
Discuss
Answer & Solution
Answer: Option C
Solution:
Slant height of cone $$ = \sqrt {{8^2} + {6^2}} = 10{\text{ cm}}$$
Slant height of cone = Radius of sector = 10 cm