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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

  • 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

  • 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

  • 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}

  • 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}

  • 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

  • 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}