Practice MCQ Questions and Answer on Volume and Surface Area

71.

Consider the volumes of the following
1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
2. A cube of each side 4 cm
3. A cylinder of radius 3 cm and length 3 cm
4. A sphere of radius 3 cm
The volumes of these in the decreasing order is :

• (A) 1, 2, 3, 4
• (B) 1, 3, 2, 4
• (C) 4, 2, 3, 1
• (D) 4, 3, 2, 1

Show Answer

 Volume of parallelepiped : $$\eqalign{ & = \left( {5 \times 3 \times 4} \right)c{m^3} \cr & = 60\,c{m^3} \cr} $$ Volume of cube : $$\eqalign{ & = {\left( 4 \right)^3}\,c{m^3} \cr & = 64\,c{m^3} \cr} $$ Volume of cylinder : $$\eqalign{ & = \left( {\frac{{22}}{7} \times 3 \times 3 \times 3} \right)c{m^3} \cr & = 84.86\,c{m^3} \cr} $$ Volume of spare : $$\eqalign{ & = \left( {\frac{4}{3} \times \frac{{22}}{7} \times 3 \times 3 \times 3} \right) \cr & = 113.14\,c{m^3} \cr} $$ So, Option D is correct decreasing order

72.

A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is :

• (A) 450
• (B) 1350
• (C) 4500
• (D) 13500

Show Answer

 $$\eqalign{ & {\text{Volume of cylinder :}} \cr & = \left( {\pi \times 3 \times 3 \times 5} \right)c{m^3} \cr & = 45\pi \,c{m^3} \cr & {\text{Volume of a cone :}} \cr & = \left( {\frac{1}{3}\pi \times \frac{1}{{10}} \times \frac{1}{{10}} \times 1} \right)c{m^3} \cr & = \frac{\pi }{{300}}\,c{m^3} \cr & \therefore {\text{Number of cones :}} \cr & = \left( {45\pi \times \frac{{300}}{\pi }} \right) \cr & = 13500 \cr} $$

73.

The curved surface area of a sphere is 5544 sq.cm. Its volume is :

• (A) 22176 cm3
• (B) 33951 cm3
• (C) 38808 cm3
• (D) 42304 cm3

Show Answer

 $$\eqalign{ & 4\pi {r^2} = 5544 \cr & \Rightarrow {r^2} = \left( {5544 \times \frac{1}{4} \times \frac{7}{{22}}} \right) \cr & \Rightarrow {r^2} = 441 \cr & \Rightarrow r = 21 \cr} $$ ∴ Volume : $$\eqalign{ & = \left( {\frac{4}{3} \times \frac{{22}}{7} \times 21 \times 21 \times 21} \right){\text{ c}}{{\text{m}}^3} \cr & = 38808{\text{ c}}{{\text{m}}^3} \cr} $$

74.

A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm so that the level may be raised 20 cm in 5 hours ?

• (A) 5000 m/hr
• (B) 5200 m/hr
• (C) 5400 m/hr
• (D) 5600 m/hr

Show Answer

 Volume flown in 5 hours : $$\eqalign{ & = \left( {225 \times 162 \times \frac{{20}}{{100}}} \right){{\text{m}}^3} \cr & = 7290\,{{\text{m}}^3} \cr} $$ Volume flown in 1 hour : $$\eqalign{ & = \left( {\frac{{7290}}{5}} \right){{\text{m}}^3} \cr & = 1458\,{{\text{m}}^3} \cr} $$ ∴ Required speed : $$\eqalign{ & = \left( {\frac{{1458}}{{0.60 \times 0.45}}} \right){\text{m/hr}} \cr & = 5400\,{\text{m/hr}} \cr} $$

75.

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients ?

• (A) 38L
• (B) 40L
• (C) 39.5L
• (D) 38.5L

Show Answer

 Diameter of bowl = 7 cm ∴ Radius of bowl = $$\frac{2}{7}$$ cm Height = 4 cm ∴ Volume of cylindrical bowl : $$\eqalign{ & = \pi {r^2}h \cr & = \frac{{22}}{7} \times \frac{7}{2} \times \frac{7}{2} \times 4 \cr & = 154\,cu.cm \cr} $$ Hence, volume of soup for 250 patients : $$\eqalign{ & = 154 \times 250 \cr & = 38500{\text{ c}}{{\text{m}}^3} \cr & = 38.5{\text{L}} \cr} $$

76.

Water flows at the rate of 10 metres per minutes from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?

• (A) 48 minutes 15 seconds
• (B) 51 minutes 12 seconds
• (C) 52 minutes 1 seconds
• (D) 55 minutes

Show Answer

 Volume flown in conical vessel : $$\eqalign{ & = \frac{1}{2}\pi \times {\left( {20} \right)^2} \times 24 \cr & = 3200\pi \cr} $$ Volume flown in 1 minute : $$\eqalign{ & = \left( {\pi \times \frac{{2.5}}{{10}} \times \frac{{2.5}}{{10}} \times 1000} \right) \cr & = 62.5\pi \cr} $$ ∴ Time taken : $$\eqalign{ & = \left( {\frac{{3200\pi }}{{62.5\pi }}} \right) \cr & = 51\operatorname{minutes} 12\operatorname{seconds} \cr} $$

77.

Given that 1 cu. cm of marble weights 25 gms, the weight of a marble block 28 cm in width and 5 cm thick is 112 kg. The length of the block is :

• (A) 26.5 cm
• (B) 32 cm
• (C) 36 cm
• (D) 37.5 cm

Show Answer

 Let length = x cm Then, $$\eqalign{ & x \times 28 \times 5 \times \frac{{25}}{{1000}} = 112 \cr & \Rightarrow x = \left( {112 \times \frac{{1000}}{{25}} \times \frac{1}{{28}} \times \frac{1}{5}} \right) \cr & \Rightarrow x = 32\,cm \cr} $$

78.

The diameter of a spare is 8 cm. It is melted and drawn into a wire of diameter 3 mm. The length of the wire is :

• (A) 36.9 m
• (B) 37.9 m
• (C) 38.9 m
• (D) 39.9 m

Show Answer

 Let the length of the wire be h Then, $$\eqalign{ & \pi \times \frac{3}{{20}} \times \frac{3}{{20}} \times h = \frac{4}{3}\pi \times 4 \times 4 \times 4 \cr & \Rightarrow h = \left( {\frac{{4 \times 4 \times 4 \times 4 \times 20 \times 20}}{{3 \times 3 \times 3}}} \right)cm \cr & \Rightarrow h = \left( {\frac{{102400}}{{27}}} \right)cm \cr & \Rightarrow h = 3792.5\,cm \cr & \Rightarrow h = 37.9\,m \cr} $$

79.

If the diameter of a sphere is 6 m, its hemisphere will have a volume of :

• (A) $$18\pi$$ m3
• (B) $$36\pi$$ m3
• (C) $$72\pi$$ m3
• (D) None of these

Show Answer

 Volume of hemisphere : $$\eqalign{ & = \left( {\frac{2}{3}\pi \times 3 \times 3 \times 3} \right){m^3} \cr & = \left( {18\pi } \right){m^3} \cr} $$

80.

A school room is be built to accommodate 70 children so as to allow 2.2 m² of floor and 11 m³ of space for each child. If the room be 14 metres long, what must be its breadth and height ?

• (A) 11 m, 4 m
• (B) 11 m, 5 m
• (C) 12 m, 5.5 m
• (D) 13 m, 6 m

Show Answer

 Let the breadth and height of the room be b and h metres respectively. Then, Area of the floor $$ = \left( {14b} \right)\,{m^2}$$ $$\eqalign{ & \therefore 14b = 2.2 \times 70 \cr & \Rightarrow b = \frac{{2.2 \times 70}}{{14}} \cr & \Rightarrow b = 11 \cr} $$ Volume of the room : $$\eqalign{ & = \left( {14 \times 11 \times h} \right){m^3} \cr & = \left( {154h} \right){m^3} \cr} $$ $$\eqalign{ & \therefore 154h = 11 \times 70 \cr & \Rightarrow h = \frac{{11 \times 70}}{{154}} \cr & \Rightarrow h = 5 \cr} $$