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Home > Practice > Arithmetic Aptitude > Volume and Surface Area > Miscellaneous

11. The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. Find the ratio of its diameter to its height.

A. 3 : 7

B. 7 : 3

C. 6 : 7

D. 7 : 6

Discuss

Solution:

\begin{aligned} \frac{π r^{2} h}{2 π r h} = \frac{924}{264} \\ \Rightarrow r = \frac{924}{264} \times 2 = 7 m \\ And, 2 π r h = 264 \\ \Rightarrow h = 264 \times \frac{7}{22} \times \frac{1}{2} \times \frac{1}{7} = 6 m \\ ∴ Required ratio \\ = \frac{2 r}{h} = \frac{14}{6} = 7 : 3 \end{aligned}

12. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

A. 90 cm

B. 1 dm

C. 1 m

D. 1.1 cm

Discuss

Solution:

Let the thickness of the bottom be x cm
Then,

(330 - 10) \times (260 - 10) \times (110 - x) =

8000 \times

1000

\Rightarrow 320 \times 250 \times (110 - x) = 8000 \times 1000

\begin{aligned} \Rightarrow (110 - x) = \frac{8000 \times 1000}{320 \times 250} = 100 \\ \Rightarrow x = 10 cm = 1 dm \end{aligned}

13. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

A. 344.35 cm²

B. 462 cm²

C. 498.35 cm²

D. None of these

Discuss

Solution:

\begin{aligned} h = 14 c m, r = 7 c m \\ So, l = \sqrt{{(7)}^{2} + {(14)}^{2}} = \sqrt{245} = 7 \sqrt{5} c m \\ ∴ Total surface area \\ = π r l + π r^{2} \\ = (\frac{22}{7} \times 7 \times 7 \sqrt{5} + \frac{22}{7} \times 7 \times 7) c m^{2} \\ = [154 (\sqrt{5} + 1)] c m^{2} \\ = (154 \times 3.236) c m^{2} \\ = 498.35 c m^{2} \end{aligned}

14. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

A. 2 : 1

B. 3 : 2

C. 25 : 18

D. 27 : 20

Discuss

Solution:

\begin{aligned} Volume of the large cube \\ = (3^{3} + 4^{3} + 5^{3}) = 216 c m^{3} \\ Let the edge of the large cube be a \\ S o, a^{3} = 216 \Rightarrow a = 6 c m \\ ∴ Required ratio \\ = \frac{6 \times (3^{2} + 4^{2} + 5^{2})}{6 \times 6^{2}} \\ = \frac{50}{36} \\ = 25 : 18 \end{aligned}

15. How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

A. 5600

B. 6000

C. 6400

D. 7200

Discuss

Solution:

\begin{aligned} Number of bricks \\ = \frac{Volume of the wall}{Volume of 1 brick} \\ = \frac{800 \times 600 \times 22.5}{25 \times 11.25 \times 6} \\ = 6400 \end{aligned}

16. The dimensions of a cuboid are 7 cm, 11 cm and 13 cm. The total surface area is :

A. 311 $c m^{2}$

B. 622 $c m^{2}$

C. 1001 $c m^{2}$

D. 2002 $c m^{2}$

Discuss

Solution:

Surface area :

\begin{aligned} = 2 (7 \times 11 + 11 \times 13 + 7 \times 13) \\ = 2 \times 311 \\ = 622 c m^{2} \end{aligned}

17. Rita and Meeta both are having lunch boxes of a cuboid shape. Length and breadth of Rita's lunch box are 10% more than that of Meeta's lunch box, but the depth of Rita's lunch box is 20% less than that of Meeta's lunch box. The ratio of the capacity of Rita's lunch box to that of Meeta's lunch box is :

A. 11 : 15

B. 15 : 11

C. 121 : 125

D. 125 : 121

Discuss

Solution:

let l, b and h denote the length, breadth and depth of Meeta's lunch box
Then, length of Rita's lunch box :

= 110 % of l = \frac{11 l}{10}

Breadth of Rita's lunch box :

= 110 % of b = \frac{11 b}{10}

Depth of Rita's lunch box :

= 80 % of h = \frac{4 h}{5}

∴ Ratio of the capacities of Rita's and Meeta's lunch boxes :

\begin{aligned} = \frac{11 l}{10} \times \frac{11 b}{10} \times \frac{4 h}{5} : l b h \\ = \frac{121}{125} : 1 \\ = 121 : 125 \end{aligned}

18. A rectangular water tank is 8 m high, 6 m long and 2.5 m wide. How many litres of water can it hold ?

A. 120 litres

B. 1200 litres

C. 12000 litres

D. 120000 litres

Discuss

Solution:

Volume of the tank :

\begin{aligned} = (8 \times 100 \times 6 \times 100 \times 2.5 \times 100) c m^{3} \\ = 120000000 c m^{3} \\ = (\frac{120000000}{1000}) litres \\ = 120000 litres \end{aligned}

19. Total surface area of a cube whose side is 0.5 cm is :

A. $\frac{1}{4} c m^{2}$

B. $\frac{1}{8} c m^{2}$

C. $\frac{3}{4} c m^{2}$

D. $\frac{3}{2} c m^{2}$

Discuss

Solution:

Surface area :

\begin{aligned} = [6 \times {(\frac{1}{2})}^{2}] c m^{2} \\ = \frac{3}{2} c m^{2} \end{aligned}

20. A larger cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. The ratio of the total surface areas of the smaller cubes and the larger cube is :

A. 2 : 1

B. 3 : 2

C. 25 : 18

D. 27 : 20

Discuss

Solution:

Volume of the larger cube :

\begin{aligned} = (3^{3} + 4^{3} + 5^{3}) c m^{3} \\ = 216 c m^{3} \end{aligned}

Let the edge of the larger cube be a cm

\begin{aligned} ∴ a^{3} = 216 \\ \Rightarrow a = 6 \end{aligned}

Required ratio :

\begin{aligned} = \frac{6 (3^{2} + 4^{2} + 5^{2})}{6 \times 6^{2}} \\ = \frac{6 \times 50}{6 \times 36} \\ = \frac{25}{18} O r 25 : 18 \end{aligned}

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