Practice MCQ Questions and Answer on Volume and Surface Area

61.

The diameter of the base of a cylindrical drum is 35 dm and the height is 24 dm. It is full of kerosene. How many tins each of size 25 cm × 22 cm × 35 cm can be filled with kerosene from the drum ?

• (A) 120
• (B) 600
• (C) 1020
• (D) 1200

Show Answer

 $$\eqalign{ & {\text{Number of tins}} \cr & = \frac{{{\text{Voulme of the drum}}}}{{{\text{Volume of each tin}}}} \cr & = \frac{{\left( {\frac{{22}}{7} \times \frac{{35}}{2} \times \frac{{35}}{2} \times 24} \right)}}{{\left( {\frac{{25}}{{10}} \times \frac{{22}}{{10}} \times \frac{{35}}{{10}}} \right)}} \cr & = 1200 \cr} $$

62.

The height of a right circular cylinder is 6 m. If three times the sum of the areas of its two circular faces is twice the area of the curved surface, then the radius of its base is :

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

Show Answer

 $$\eqalign{ & 3 \times 2\pi {r^2} = 2 \times 2\pi rh \cr & \Rightarrow 6r = 4h \cr & \Rightarrow r = \frac{2}{3}h \cr & \Rightarrow r = \left( {\frac{2}{3} \times 6} \right)m \cr & \Rightarrow r = 4\,m \cr} $$

63.

The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is :

• (A) 1 : 1
• (B) 1 : 2
• (C) 2 : 1
• (D) 2 : 3

Show Answer

 Let the radius of the sphere be r Then, radius of the cylinder = r Height of the cylinder = 2r Surface area of sphere = $$4\pi {{\text{r}}^2}$$ Surface area of the cylinder = $$2\pi {\text{r}}(2r) = 4\pi {{\text{r}}^2}$$ ∴ Required ratio : = $$4\pi {{\text{r}}^2}$$ : $$4\pi {{\text{r}}^2}$$ = 1 : 1

64.

A rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper. The radius of the base of the cylinder so rolled is :

• (A) 3.5 cm
• (B) 5 cm
• (C) 7 cm
• (D) 14 cm

Show Answer

 Length of rectangle paper = Circumference of the base of cylinder If r is the radius of the cylinder : $$\eqalign{ & \Rightarrow 44 = 2\pi r \cr & \Rightarrow r = \frac{{44 \times 7}}{{2 \times 22}} \cr & \Rightarrow r = 7\,cm \cr} $$

65.

An aluminium sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference in the surface areas of the two solids would be :

• (A) Nil
• (B) 284 cm2
• (C) 286 cm2
• (D) 296 cm2

Show Answer

 Volume of cube = Volume of sheet = (27 × 8 × 1) cm3 = 216 cm3 Edge of cube : $$\root 3 \of {216} \,cm = 6\,cm$$ Surface area of sheet : $$\eqalign{ & = 2\left( lb + bh + lh \right) \cr & = 2\left( {27 \times 8 + 8 \times 1 + 27 \times 1} \right){\text{ c}}{{\text{m}}^2} \cr & = \left( {216 + 8 + 27} \right){\text{ c}}{{\text{m}}^2} \cr & = 502{\text{ c}}{{\text{m}}^2} \cr} $$ Surface area of cube : $$\eqalign{ & = 6{a^2} \cr & = \left( {6 \times {6^2}} \right){\text{ c}}{{\text{m}}^2} \cr & = 216{\text{ c}}{{\text{m}}^2} \cr} $$ ∴ Required difference : $$\eqalign{ & = \left( {502 - 216} \right){\text{ c}}{{\text{m}}^2} \cr & = 286{\text{ c}}{{\text{m}}^2} \cr} $$

66.

A copper wire of length 36 m and diameter 2 mm is melted to form a sphere. The radius of the sphere (in cm) is :

• (A) 2.5 cm
• (B) 3 cm
• (C) 3.5 cm
• (D) 4 cm

Show Answer

 Let the radius of the sphere be r cm Then, $$\eqalign{ & \frac{4}{3}\pi {r^3} = \pi \times {\left( {0.1} \right)^2} \times 3600 \cr & \Leftrightarrow {r^3} = 36 \times \frac{3}{4} \cr & \Leftrightarrow {r^3} = 27 \cr & \Leftrightarrow r = 3\,cm \cr} $$

67.

A larger cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. The ratio of the total surface areas of the smaller cubes and the larger cube is :

• (A) 2 : 1
• (B) 3 : 2
• (C) 25 : 18
• (D) 27 : 20

Show Answer

 Volume of the larger cube : $$\eqalign{ & = \left( {{3^3} + {4^3} + {5^3}} \right){\text{ c}}{{\text{m}}^3} \cr & = 216{\text{ c}}{{\text{m}}^3} \cr} $$ Let the edge of the larger cube be a cm $$\eqalign{ & \therefore {a^3} = 216 \cr & \Rightarrow a = 6 \cr} $$ Required ratio : $$\eqalign{ & = \frac{{6\left( {{3^2} + {4^2} + {5^2}} \right)}}{{6 \times {6^2}}} \cr & = \frac{{6 \times 50}}{{6 \times 36}} \cr & = \frac{{25}}{{18}}\,Or\,25:18 \cr} $$

68.

A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. It volume is :

• (A) 208 m3
• (B) 270 m3
• (C) 360 m3
• (D) 408 m3

Show Answer

 Volume : $$\eqalign{ & = \left[ {12 \times 9 \times \left( {\frac{{1 + 4}}{2}} \right)} \right]{m^3} \cr & = \left( {12 \times 9 \times 2.5} \right){m^3} \cr & = 270\,{m^3} \cr} $$

69.

How many small cubes, each of 96 cm surface area, can be formed from the material obtained by melting a larger cube of 384 cm surface area ?

• (A) 5
• (B) 8
• (C) 800
• (D) 8000

Show Answer

 Let the length of each edge of small cube be a1 and that of larger cube be a2 Then, $$\eqalign{ & 6a_1^2 = 96\, \cr & \Rightarrow a_1^2 = 16 \cr & \Rightarrow {a_1} = 4\,and \cr & 6a_2^2 = 384 \cr & \Rightarrow a_2^2 = 64 \cr & \Rightarrow {a_2} = 8 \cr} $$ ∴ Number of cubes formed : $$\eqalign{ & = \frac{{{\text{Volume of larger cube}}}}{{{\text{Volume of smaller cube}}}} \cr & = \left( {\frac{{8 \times 8 \times 8}}{{4 \times 4 \times 4}}} \right) \cr & = 8 \cr} $$

70.

The radius of a hemispherical bowls is 6 cm. The capacity of the bowl is $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$

• (A) 495.51 cm3
• (B) 452.57 cm3
• (C) 345.53 cm3
• (D) 422 cm3

Show Answer

 Radius of hemisphere bowl = 6 cm ∴ Volume of hemisphere : $$\eqalign{ & = \frac{2}{3}\pi {r^3} \cr & = \frac{2}{3} \times \frac{{22}}{7} \times 6 \times 6 \times 6 \cr & = \frac{{9504}}{{21}} \cr & = 452.57{\text{ c}}{{\text{m}}^3} \cr} $$