Practice | Hashtable

content Computer Science Arithmetic Aptitude Data Interpretation Logical Reasoning Verbal Reasoning Non-Verbal Reasoning

About About Privacy Policy

Hashtable

Home
Practice
PYQ
Mock Test
Register Free

Home Practice PYQ Mock Test Register Free

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

1. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

A. 12 $π$ cm³

B. 15 $π$ cm³

C. 16 $π$ cm³

D. 20 $π$ cm³

Discuss

Solution:

\begin{aligned} Clearly, \\ We have r = 3 cm and h = 4 cm \\ ∴ Volume \\ = \frac{1}{3} π r^{2} h \\ = (\frac{1}{3} \times π \times 3^{2} \times 4) c m^{3} \\ = 12 π c m^{3} \end{aligned}

2. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

A. 75 cu. m

B. 750 cu. m

C. 7500 cu. m

D. 75000 cu. m

Discuss

Solution:

\begin{aligned} 1 hectare = 10000 m^{2} \\ So, Area = (1.5 \times 10000) m^{2} \\ = 15000 m^{2} \\ Depth = \frac{5}{100} m = \frac{1}{20} m \\ ∴ Volume = (Area \times Depth) \\ = (15000 \times \frac{1}{20}) m^{3} \\ = 750 m^{3} \end{aligned}

3. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

A. 720 m³

B. 900 m³

C. 1200 m³

D. 1800 m³

Discuss

Solution:

\begin{aligned} 2 (15 + 12) \times h = 2 (15 \times 12) \\ \Rightarrow h = \frac{180}{27} m = \frac{20}{3} m \\ ∴ Volume = (15 \times 12 \times \frac{20}{3}) m^{3} \\ = 1200 m^{3} \end{aligned}

4. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

A. 84 meters

B. 90 meters

C. 168 meters

D. 336 meters

Discuss

Solution:

\begin{aligned} Let the length of the wire be h \\ Radius = \frac{1}{2} m m = \frac{1}{20} c m . Then, \\ \Rightarrow \frac{22}{7} \times \frac{1}{20} \times \frac{1}{20} \times h = 66 \\ \Rightarrow h = \frac{66 \times 20 \times 20 \times 7}{22} \\ = 8400 c m \\ = 84 m e t e r s \end{aligned}

5. 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 8 g/cm³, then the weight of the pipe is:

A. 3.6 kg

B. 3.696 kg

C. 36 kg

D. 36.9 kg

Discuss

Solution:

\begin{aligned} External radius = 4 c m \\ Internal radius = 3 c m \\ Volume of iron \\ = (\frac{22}{7} \times [{(4)}^{2} - {(3)}^{2}] \times 21) c m^{3} \\ = (\frac{22}{7} \times 7 \times 1 \times 21) c m^{3} \\ = 462 c m^{3} \\ ∴ Weight of iron = (462 \times 8) g m \\ = 3696 g m \\ = 3.696 k g \end{aligned}

6. 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 on it. The mass of the man is:

A. 12 kg

B. 60 kg

C. 72 kg

D. 96 kg

Discuss

Solution:

Volume of water displaced
= (3 x 2 x 0.01) m³
= 0.06 m³.
∴ Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.

7. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m³, then the rise in the water level in the tank will be:

A. 20 cm

B. 25 cm

C. 35 cm

D. 50 cm

Discuss

Solution:

\begin{aligned} Total Volume of water displaced \\ = (4 \times 50) m^{3} = 200 m^{3} \\ ∴ Rise in water level \\ = (\frac{200}{40 \times 20}) m \\ = 0.25 m \\ = 25 c m \end{aligned}

8. The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

A. 30π m²

B. 40π m²

C. 60π m²

D. 80π m²

Discuss

Solution:

\begin{aligned} l = 10 m \\ h = 8 m \\ S o, r = \sqrt{l^{2} - h^{2}} = \sqrt{{(10)}^{2} - 8^{2}} = 6 m \\ ∴ Curved surface area \\ π r l = (π \times 6 \times 10) m^{2} \\ = 60 π m^{2} \end{aligned}

9. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

A. 49 m²

B. 50 m²

C. 53.5 m²

D. 55 m²

Discuss

Solution:

\begin{aligned} Area of the wet surface \\ = [2 (l b + b h + l h) - l b] \\ = 2 (b h + l h) + l b \\ = [2 (4 \times 1.25 + 6 \times 1.25) + 6 \times 4] m^{2} \\ = 49 m^{2} \end{aligned}

10. A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m³) is:

A. 4830

B. 5120

C. 6420

D. 8960

Discuss

Solution:

Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
∴ Volume of the box
= (32 x 20 x 8) m³
= 5120 m³

1 2 3 4 5 6 7 8 9 10

Sign up for our newsletter

Are you passionate about opportunities in the realm of Computer Science within the government sector? Don't miss out on crucial updates, job openings, and career prospects tailored specifically straight to your inbox.

Email address

By subscribing, you agree with our Terms of Service and Privacy Policy.

Resources

Practice PYQ Mock Test

Company

About us Contact us Privacy policy Terms of service

Hashtable