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Volume and Surface Area Questions Answers

Volume and Surface Area Questions Answers (MCQ) listings with explanations includes questions on Cubiod, Cube, Cylinder, Cone, Sphere, Hemisphere etc which are important for competitive exams like SSC, BANK PO, Clerk, IBPS, SBI-PO, RBI, MBA, MAT, CAT, IIFT, IGNOU, SSC CGL, CBI, CPO, CLAT, CTET, NDA, CDS, Specialist Officers.

1) If the volume of two cubes are in the ratio 27:1, the ratio of their edges i

  • 1) 3:1
  • 2) 3:2
  • 3) 3:5
  • 4) 3:7
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Ans.   A
Explanation :
Let the edges be a and b of two cubes, then \begin{aligned} \frac{a^3}{b^3} = \frac{27}{1} \=> \left( \frac{a}{b} \right)^3 = \left( \frac{3}{1} \right)^3 \\frac{a}{b}=\frac{3}{1} \=> a:b = 3:1 \end{aligned}

2) A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug o

  • 1) \begin{aligned} 40 m^3 \end{aligned}
  • 2) \begin{aligned} 42 m^3 \end{aligned}
  • 3) \begin{aligned} 44 m^3 \end{aligned}
  • 4) \begin{aligned} 46 m^3 \end{aligned}
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Ans.   C
Explanation :
\begin{aligned} Volume = \pi r^2h \Volume = \left(\frac{22}{7}*1*1*14\right)m^3 \= 44 m^3 \end{aligned}

3) Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radi

  • 1) \begin{aligned} \sqrt{3}:1 \end{aligned}
  • 2) \begin{aligned} \sqrt{7}:1 \end{aligned}
  • 3) \begin{aligned} \sqrt{2}:1 \end{aligned}
  • 4) \begin{aligned} 2:1 \end{aligned}
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Ans.   C
Explanation :
Let their heights be h and 2h and radii be r and R respectively then. \begin{aligned} \pi r^2h = \pi R^2(2h) \=> \frac{r^2}{R^2} = \frac{2h}{h} \= \frac{2}{1} \=> \frac{r}{R} = \frac{\sqrt{2}}{1} \=> r:R = \sqrt{2}:1 \\end{aligned}

4) A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop

  • 1) \begin{aligned} 11\frac{3}{7} cm \end{aligned}
  • 2) \begin{aligned} 11\frac{2}{7} cm \end{aligned}
  • 3) \begin{aligned} 11\frac{1}{7} cm\end{aligned}
  • 4) \begin{aligned} 11 cm\end{aligned}
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Ans.   A
Explanation :
Let the drop in the water level be h cm, then, \begin{aligned} \text{Volume of cylinder= }\pi r^2h \=> \frac{22}{7}*\frac{35}{2}*\frac{35}{2}*h = 11000 \=> h = \frac{11000*7*4}{22*35*35}cm\= \frac{80}{7}cm\= 11\frac{3}{7} cm \end{aligned}

5) 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length if the wire in meters will b

  • 1) 76 m
  • 2) 80 m
  • 3) 84 m
  • 4) 88 m
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Ans.   C
Explanation :
Let the length of the wire be h \begin{aligned} Radius = \frac{1}{2}mm = \frac{1}{20}cm\\pi r^2h = 66 \\frac{22}{7}*\frac{1}{20}*\frac{1}{20}*h = 66 \=> h = \frac{66*20*20*7}{22} \= 8400 cm \= 84 m \end{aligned}

6) A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights 8g/cm cube, then find the weight of the pip

  • 1) 3.696 kg
  • 2) 3.686 kg
  • 3) 2.696 kg
  • 4) 2.686 kg
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Ans.   A
Explanation :
In this type of question, we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow. Oh! line become a bit complicated, sorry for that, lets solve it. External radius = 4 cm Internal radius = 3 cm [because thickness of pipe is 1 cm] \begin{aligned} \text{Volume of iron =}\pi r^2h\= \frac{22}{7}*[4^2 - 3^2]*21 cm^3\= \frac{22}{7}*1*21 cm^3\= 462 cm^3 \\end{aligned} Weight of iron = 462*8 = 3696 gm = 3.696 kg

7) How many cubes of 10 cm edge can be put in a cubical box of 1 m edg

  • 1) 10000 cubes
  • 2) 1000 cubes
  • 3) 100 cubes
  • 4) 50 cubes
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Ans.   B
Explanation :
\begin{aligned} \text{Number of cubes =}\frac{100*100*100}{10*10*10} \= 1000 \end{aligned} Note: 1 m = 100 cm

8) The curved surface of a right circular cone of height 15 cm and base diameter 16 cm

  • 1) \begin{aligned} 116 \pi cm^2 \end{aligned}
  • 2) \begin{aligned} 122 \pi cm^2 \end{aligned}
  • 3) \begin{aligned} 124 \pi cm^2 \end{aligned}
  • 4) \begin{aligned} 136 \pi cm^2 \end{aligned}
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Ans.   D
Explanation :
\begin{aligned} \text{Curved surface area of cone=}\pi rl\l = \sqrt{r^2+h^2} \l = \sqrt{8^2+15^2} = 17cm \ \text{Curved surface area =}\pi rl\= \pi *8*17 = 136 \pi cm^2 \end{aligned}

9) If a right circular cone of height 24 cm has a volume of 1232 cm cube, then the area of its curved surface i

  • 1) \begin{aligned} 450 cm^2 \end{aligned}
  • 2) \begin{aligned} 550 cm^2 \end{aligned}
  • 3) \begin{aligned} 650 cm^2 \end{aligned}
  • 4) \begin{aligned} 750 cm^2 \end{aligned}
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Ans.   B
Explanation :
Volume is given, we can calculate the radius from it, then by calculating slant height, we can get curved surface area. \begin{aligned} \frac{1}{3}*\pi *r^2*h = 1232 \\frac{1}{3}*\frac{22}{7}*r^2*24 = 1232 \r^2 = \frac{1232*7*3}{22*24} = 49 \r = 7 \\text{Now, r = 7cm and h = 24 cm } \l = \sqrt{r^2+h^2} \= \sqrt{7^2+24^2} = 25cm \\text{Curved surface area =}\pi rl\= \frac{22}{7}*7*25 = 550 cm^2 \end{aligned}

10) A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube)

  • 1) 4120 m cube
  • 2) 4140 m cube
  • 3) 5140 m cube
  • 4) 5120 m cube
View Answer View Explanation
Ans.   D
Explanation :
l = (48 - 16)m = 32 m, [because 8+8 = 16] b = (36 -16)m = 20 m, h = 8 m. Volume of the box = (32 x 20 x 8) m cube = 5120 m cube.
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