# 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}

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