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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 7 Mensuration Ex 7.2

10th Maths Exercise 7.2 Samacheer Kalvi Question 1.
A 14 m deep well with inner diameter 10 m is dug and the earth taken out is evenly spread all around the well to form an embankment of width 5 m. Find the height of the embankment.
Solution:
Inner diameter = 10 m
Inner radius = 5 m
Inner height = 14 m
10th Maths Exercise 7.2 Samacheer Kalvi Chapter 7 Mensuration
Volume of the cylinder = πr2h cubic units
\(=\frac{22}{7} \times 5 \times 5 \times 14\)
= 1100 m3
Volume of the hollow = n(R2 – r2)h cubic units
R = 10 m
r = 5 m
\(\Rightarrow \frac{22}{7} \times\left(10^{2}-5^{2}\right) h=1100 \mathrm{m}^{3}\)
(∵ the earth taken out = the earth spread all around)
Exercise 7.2 Class 10 Samacheer Kalvi Maths Solutions Chapter 7 Mensuration

Exercise 7.2 Class 10 Samacheer Kalvi Question 2.
A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of radius 5 cm and height 4 cm is immersed it completely. Calculate the raise of the water in the glass?
Solution:
The volume of the water raised = Volume of the cylindrical metal.
Ex 7.2 Class 10 Samacheer Kalvi Chapter 7 Mensuration
∴ The height of the raised water in the glass = 1 cm.

Ex 7.2 Class 10 Samacheer Question 3.
If the circumference of a conical wooden piece is 484 cm then find its volume when its height is 105 cm.
Solution:
Circumference of the base of the cone = 484 cm
height = 105 cm
∴ 2πr = 484
10th Maths Mensuration Exercise 7.2 Samacheer Kalvi Chapter 7
\(r=484 \times \frac{1}{2} \times \frac{7}{22}\)
= 77 cm
Samacheer Kalvi 10th Maths Chapter 7 Mensuration Ex 7.2 5

10th Maths Mensuration Exercise 7.2 Question 4.
A conical container is fully filled with petrol. The radius is 10m and the height is 15 m. If the container can release the petrol through its bottom at the rate of 25 cu. meter per minute, in how many minutes the container will be emptied. Round off your answer to the nearest minute.
Solution:
Volume of the cone = \(\frac{1}{3} \pi r^{2} h\) cu. units.
10th Maths Exercise 7.2 Samacheer Kalvi Chapter 7 Mensuration
Volume of the given conical container = \(\frac{1}{3} \times \pi \times 10 \times 10 \times 15\)
= 500π m3
10th Maths Exercise 7.2 In Tamil Samacheer Kalvi Chapter 7 Mensuration

10th Maths Exercise 7.2 Question 5.
A right angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed.
Solution:
When the triangle ABC is rotated about AB, the
10th Maths 7.2 Exercise Samacheer Kalvi Solutions Chapter 7 Mensuration

10th Maths Exercise 7.2 In Tamil Question 6.
The volumes of two cones of same base radius are 3600 cm3 and 5040 cm3. Find the ratio of heights.
Solution:
Samacheer Kalvi 10th Maths Mensuration Chapter 7 Ex 7.2

10th Maths 7.2 Exercise Question 7.
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
Solution:
9th Maths Exercise 7.2 Samacheer Kalvi Chapter 7 Mensuration

Samacheer Kalvi 10th Maths Mensuration Question 8.
A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is \(3 \sqrt{3} : 4\)
Solution:
10th Class Maths Exercise 7.2 Samacheer Kalvi Chapter 7 Mensuration

9th Maths Exercise 7.2 Samacheer Kalvi Question 9.
The outer and the inner surface areas of a spherical copper shell are 576π cm2 and 324π cm2 respectively. Find the volume of the material required to make the shell.
Solution:
Class 10 Maths Exercise 7.2 Solutions Samacheer Kalvi Chapter 7 Mensuration
9th Standard Maths Exercise 7.2 In Tamil Samacheer Kalvi Chapter 7 Mensuration

10th Class Maths Exercise 7.2 Question 10.
A container open at the top is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill a container at the rate of ₹ 40 per litre.
Solution:
Volume of the frustum
10th Maths Chapter 7 Exercise 7.2 Samacheer Kalvi Mensuration
Solution Of Exercise 7.2 Maths Class 10 Samacheer Kalvi Chapter 7 Mensuration

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