Chapter 9 Mensuration Ex 9.3 NCERT Solutions for Class 8 Maths

Latest Updated : November 2023

If you are in search of NCERT solutions for Class 8 Maths Chapter 9 Mensuration, then you are at the right place. When it comes to Mathematics, it is a subject that holds value for students across various academic streams, be it science, biology, or commerce and having a very good understanding of basic math concepts will help you in achieving your goal and make it much more easier.

Here we provide detailed NCERT solutions for Class 8 Maths of all the chapters, exercise wise with updated syllabus by NCERT. These NCERT solutions for Class 8 Maths have been carefully crafted to provide detailed explanations, ensuring that students can grasp the concepts effectively. We also provide extra practice questions for the same, so feel free to bookmark ncertforclass8.com to boost your preparation.

NCERT Solutions for Class 8 Maths Chapter 9 Mensuration Ex 9.3

NCERT Solutions for Class 8 Maths Chapter 9 Mensuration Ex 9.3

Class 8 Maths Chapter 9 Mensuration Exercise 9.3

Exercise 9.3

1. Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.

Solution:

We find area when a region covered by a boundary, such as outer and inner surface area of a cylinder, a cone, a sphere and surface of wall or floor.
When the amount of space occupied by an object such as water, milk, coffee, tea, etc., then we have to find out volume of the object.
(a) Volume
(b) Surface area
(c) Volume

2. Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

Solution:

Yes, we can say that volume of cylinder B is greater as the radius of cylinder B is greater than that of cylinder A. Therefore greater radius will give us a greater volume.

Volume of A-
Diameter of cylinder A = 7 cm
Radius of cylinder A = 7/2 cm
Height of cylinder A = 14 cm

\[Volume\ of\ cylinder\ A=\ \pi r^2h\]

\[=\frac{22}{7}\times\frac{7}{2}\times\frac{7}{2}\times14=539\ cm^3\]

\[Volume\ of\ cylinder\ A\ is\ 539\ cm^3\]

Volume of B-
Diameter of cylinder B = 14 cm
Radius of cylinder B = 14/2 = 7 cm
Height of cylinder B = 7 cm

\[Volume\ of\ cylinder\ B=\ \pi r^2h\]

\[=\frac{22}{7}\times7\times7\times7=1078\ cm^3\]

\[Volume\ of\ cylinder\ B\ is\ 1078\ cm^3\]

Surface area of cylinder A-

\[Surface\ area\ of\ cylinder\ A=2\pi r(r+h)\]

\[=2\times\frac{22}{7}\ \times\frac{7}{2}\times\left(\frac{7}{2}+14\right)=385\ cm^2\]

Surface area of cylinder B-

\[Surface\ area\ of\ cylinder\ B=2\pi r(r+h)\]

\[=2\times\frac{22}{7}\times7(\ 7+7)=616\ cm^2\]

Yes, the cylinder with greater volume also has a greater surface area.

3. Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?

Solution:

Base area of cuboid = 180 cm2 [Given]
Volume of cuboid = 900 cm3 [Given]

We know that, Volume of cuboid = lbh

900 = 180×h

\[h\ =\ \frac{900}{180}\ =\ 5\ cm\]

Hence the height of the cuboid is 5 cm.

4. A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Solution:

Length of cuboid (l) = 60 cm [Given]
Breadth of cuboid (b) = 54 cm [Given]
Height of cuboid (h) = 30 cm [Given]

\[We\ know\ that,\ Volume\ of\ cuboid=lbh\]

\[=60\times54\times30=97200\ cm^3\]

\[Volume\ of\ cube=(Side)^3\]

\[=6\times6\times6=216\ cm^3\]

\[Also\ ,the\ Number\ of\ small\ cubes=\frac{volume\ of\ cuboid}{volume\ of\ cube}\]

\[=\frac{97200}{216}=\ 450\ cubes\]

Hence , the required number of cubes is 450.

5. Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm ?

Solution:

\[Volume\ of\ cylinder=1.54\ m^3\ \ \left[Given\right]\]

Diameter (d) of cylinder = 140 cm [Given]
Radius ( r )= d/2 = 140/2 = 70 cm [Given]

\[Volume\ of\ cylinder=\pi r^2h\]

\[1.54=\frac{22}{7}\times0.7\times0.7\times h\]

\[h=\frac{\left(1.54\times7\right)}{(22\times0.7\times0.7)}\ =\ 1\ m\]

Hence, the height of the cylinder is 1 m.

6. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?

Solution:

Radius of cylindrical tank (r) = 1.5 m
Height of cylindrical tank (h) = 7 m

\[Volume\ of\ cylindrical\ \tan k\ \ \ (V)\ \ =\pi r^2h\]

\[=\frac{22}{7}\times1.5\times1.5\times7\ =49.5\ cm^3\]

\[=49.5\times1000\ liters=49500\ \ liters\ \ \ \ [∵\ 1\ m^3=1000\ litres]\]

Hence, the required quantity of milk is 49500 litres.

7. If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(ii) how many times will its volume increase?

Solution:

(i) Let the edge of the cube be “ l” .

\[Surface\ area\ of\ the\ cube\ \left(A\right)\ =6l^2\]

\[When\ the\ edge\ of\ the\ cube\ 'l'\ is\ doubled,\ then\]

\[Surface\ area\ of\ the\ cube,\ say\ A’=6(2l)^2=6\times4l^2=4\times(6l^2)\]

\[A’=4\ \times A\]

\[Hence,\ the\ surface\ area\ will\ increase\ by\ four\ times.\]

\[(ii)\ Volume\ of\ a\ cube\ \left(V\right)=l^3\]

\[When\ the\ edge\ of\ the\ cube\ 'l'\ is\ doubled,\ then\]

\[Volume\ of\ the\ cube\ ,\ say\ V\ ’=(2l)^3=8(l^3)\]

\[V\ ’=8\times V\]

\[Hence,\ the\ volume\ will\ increase\ 8\ times.\]

8. Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.

Solution:

\[The\ \ volume\ of\ the\ reservoir=108\ m^3\]

\[Rate\ of\ pouring\ water\ into\ cuboidal\ reservoir=60\ litres/\min\]

\[=\frac{60}{1000}m^3\ per\min\ \ \ \ \ \left[∵\ 1\ liter=\frac{1}{1000}\ m^3\right]\]

\[=\frac{\left(60\times60\right)}{1000}\ m^3\ per\ hour\]

\[Therefore,\frac{\left(60\times60\right)}{1000}\ m^3\ water\ filled\ in\ reservoir\ will\ take=1\ hour\]

\[Therefore\ 1\ m^3\ water\ filled\ in\ reservoir\ will\ take=\frac{1000}{60\ \times60}\ hours\]

\[Therefore,\ 108\ m^3\ water\ filled\ in\ reservoir\ will\ take=\frac{\left(108\times1000\right)}{(60\times60)}hours=30\ hours\]

Hence, It will take 30 hours to fill the reservoir.

Using Class 8 NCERT solutions offers several key advantages for students:

  1. Accurate Answers: NCERT solutions for Class 8 Maths are prepared by expert educators and thoroughly reviewed to ensure quality and accurate answers.
  2. Aligned with Curriculum: NCERT Solutions for Class 8 Maths are specifically designed to go along with the CBSE curriculum, making them the ideal resource for students studying in CBSE affiliated schools.
  3. Crisp an Clear Explanation: The NCERT solutions for Class 8 Maths provide step by step explanations, making complex concepts easier to understand. This helps students to grasp the concepts easily and build a better foundation.
  4. Time-Saver: Instead of spending extra time searching for answers, students can quickly access these NCERT solutions for Class 8 Maths , saving time and allowing them to focus on other aspects of their studies.
  5. Extra Questions: NCERT Solutions for Class 8 Maths also has extra questions that offer additional opportunities for students to build better problem solving skills.
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