Volume and Surface Area Questions Answers

• 1. 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 And Explanation

  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

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• 2. A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm. Find the total area of the wet surface.

  1. 42 m sqaure
  2. 49 m sqaure
  3. 52 m sqaure
  4. 64 m sqaure

  Answer And Explanation

  Answer: Option B

  Explanation:

  Area of the wet surface =
  2[lb+bh+hl] - lb = 2 [bh+hl] + lb
  = 2[(4*1.25+6*1.25)]+6*4 = 49 m square

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• 3. 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 And Explanation

  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

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• 4. 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 And Explanation

  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 =
  $$\begin{aligned} \frac{\text{Volume of wall}}{\text{Volume of 1 brick}} \\ = \frac{800*600*22.5}{25*11.25*6} \\ = 6400 \end{aligned}$$

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• 5. 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. Its volume is:

  1. 260
  2. 262
  3. 270
  4. 272

  Answer And Explanation

  Answer: Option C

  Explanation:

  Volume will be length * breadth * height, but in this case two heights are given so we will take average,
  
  $$\begin{aligned} Volume = \left(12*9*\left(\frac{1+4}{2}\right)\right)m^3 \\ 12*9*2.5 m^3 = 270 m^3 \end{aligned}$$

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• 6. 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 And Explanation

  Answer: Option A

  Explanation:

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

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• 7. The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side.

  1. Rs. 850
  2. Rs. 860
  3. Rs. 876
  4. Rs. 886

  Answer And Explanation

  Answer: Option C

  Explanation:

  We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.
  Here we go,
  
  $$\begin{aligned} \text{Surface area =}6a^2 \\ = 6 * 8^2 = 384 \text{sq feet} \\ \text{Quantity required =}\frac{384}{16} \\ = 24 kg\\ \text{Cost of painting =} 36.50*24 \\ = Rs. 876 \end{aligned}$$

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