Volume and Surface Area Problems and Solutions

• 22. A hollow spherical metallic ball has an external diameter 6 cm and is 1/2 cm thick. The volume of metal used in the metal is:

  1. \begin{aligned} 47\frac{1}{5} cm^3 \end{aligned}
  2. \begin{aligned} 47\frac{3}{5} cm^3 \end{aligned}
  3. \begin{aligned} 47\frac{7}{5} cm^3 \end{aligned}
  4. \begin{aligned} 47\frac{9}{5} cm^3 \end{aligned}

  Answer :

  Option B

  Explanation:

  Please note we are talking about "Hollow" ball. Do not ignore this word in this type of question in a hurry to solve this question.
  If we are given with external radius and thickness, we can get the internal radius by subtracting them. Then the volume of metal can be obtained by its formula as,
  
  External radius = 3 cm,
  Internal radius = (3-0.5) cm = 2.5 cm
  
  \begin{aligned}
  \text{Volume of sphere =}\frac{4}{3}\pi r^3 \\
  = \frac{4}{3}*\frac{22}{7}*[3^2 - 2.5^2]cm^3 \\
  = \frac{4}{3}*\frac{22}{7}*\frac{91}{8}cm^3 \\
  = \frac{143}{3} cm^3 \\
  = 47\frac{2}{3}cm^3
  \end{aligned}

• 23. The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is:

  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}

  Answer :

  Option 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}

• 24. A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is :

  1. 50 kg
  2. 60 kg
  3. 70 kg
  4. 80 kg

  Answer :

  Option B

  Explanation:

  In this type of question, first we will calculate the volume of water displaces then will multiply with the density of water.
  Volume of water displaced = 3*2*0.01 = 0.06 m cube
  
  Mass of Man = Volume of water displaced * Density of water
  
  = 0.06 * 1000 = 60 kg

• 25. 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 :

  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

• 26. Find the surface area of a 10cm*4cm*3cm brick.

  1. 154 cm square
  2. 156 cm square
  3. 160 cm square
  4. 164 cm square

  Answer :

  Option D

  Explanation:

  Surface area of a cuboid = 2(lb+bh+hl) cm square
  So,
  Surface area of a brick = 2(10*4+4*3+3*10) cm square
  = 2(82) cm square = 164 cm square