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Volume and Surface Area Questions Answers

  • 8. How many cubes of 10 cm edge can be put in a cubical box of 1 m edge.

    1. 10000 cubes
    2. 1000 cubes
    3. 100 cubes
    4. 50 cubes
    Answer And Explanation

    Answer: Option B

    Explanation:

    \begin{aligned}
    \text{Number of cubes =}\frac{100*100*100}{10*10*10} \\
    = 1000
    \end{aligned}

    Note: 1 m = 100 cm

  • 9. If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:

    1. 3:1
    2. 3:2
    3. 3:5
    4. 3:7
    Answer And Explanation

    Answer: Option 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}

  • 10. 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 out.

    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}
    Answer And Explanation

    Answer: Option C

    Explanation:

    \begin{aligned}
    Volume = \pi r^2h \\
    Volume = \left(\frac{22}{7}*1*1*14\right)m^3 \\
    = 44 m^3
    \end{aligned}

  • 11. Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.

    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}
    Answer And Explanation

    Answer: Option 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}

  • 12. 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 by:

    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}
    Answer And Explanation

    Answer: Option 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}

  • 13. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length if the wire in meters will be:

    1. 76 m
    2. 80 m
    3. 84 m
    4. 88 m
    Answer And Explanation

    Answer: Option 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}

  • 14. 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 pipe.

    1. 3.696 kg
    2. 3.686 kg
    3. 2.696 kg
    4. 2.686 kg
    Answer And Explanation

    Answer: Option 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