Volume and Surface Area Problems and Solutions

• 1. 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 :

  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}

• 2. The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:

  1. 4 cm
  2. 6 cm
  3. 8 cm
  4. 10 cm

  Answer :

  Option B

  Explanation:

  \begin{aligned}
  \text{Curved surface area of sphere =}\\
  \frac{4}\pi r^2 \\
  \text{Surface area of cylinder =} \\
  2\pi rh \\
  => \frac{4}\pi r^2 = 2\pi rh \\
  => r^2 = \frac{6*12}{2} \\
  => r^2 = 36 \\
  => r = 6
  \end{aligned}
  
  Note: Diameter of cylinder is 12 so radius is taken as 6.

• 3. 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 :

  Option B

  Explanation:

  \begin{aligned}
  \text{Number of cubes =}\frac{100*100*100}{10*10*10} \\
  = 1000
  \end{aligned}
  
  Note: 1 m = 100 cm

• 4. A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :

  1. 45%
  2. 56%
  3. 67%
  4. 75%

  Answer :

  Option D

  Explanation:

  We will first subtract the cone volume from wood volume to get the wood wasted.
  Then we can calculate its percentage.
  
  \begin{aligned}
  \text{Sphere Volume =}\frac{4}{3}\pi r^3 \\
  \text{Cone Volume =}\frac{1}{3}\pi r^2h\\
  
  \text{Volume of wood wasted =}\\
  \left(\frac{4}{3}\pi *9*9*9\right)-\left(\frac{1}{3}\pi *9*9*9\right) \\
  = \pi *9*9*9 cm^3 \\
  \text{Required Percentage =} \\
  \frac{\pi *9*9*9}{\frac{4}{3}\pi *9*9*9}*100 \% \\
  = \frac{3}{4}*100 \% \\
  = 75\%
  \end{aligned}

• 5. How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.5m

  1. 6100
  2. 6200
  3. 6300
  4. 6400

  Answer :

  Option D

  Explanation:

  To solve this type of question, simply divide the volume of wall with the volume of brick to get the numbers of required bricks
  So lets solve this
  
  Number of bricks =
  \begin{aligned}
  \frac{\text{Volume of wall}}{\text{Volume of 1 brick}} \\
  = \frac{800*600*22.5}{25*11.25*6} \\
  = 6400
  \end{aligned}

• 6. 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 :

  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}

• 7. The perimeter of one face of a cube is 20 cm. Its volume will be:

  1. \begin{aligned} 125 cm^3 \end{aligned}
  2. \begin{aligned} 400 cm^3 \end{aligned}
  3. \begin{aligned} 250 cm^3 \end{aligned}
  4. \begin{aligned} 625 cm^3 \end{aligned}

  Answer :

  Option A

  Explanation:

  Edge of cude = 20/4 = 5 cm
  
  Volume = a*a*a = 5*5*5 = 125 cm cube