In Fig. 13.12, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
Solution:
Given: The frame has a base diameter of 20 cm and height of 30 cm.
Since the frame is cylindrical in shape, the cloth required to cover the lampshade will be equal to the curved surface area of cylinder.
The amount of cloth required to cover the cylinder will be equal to the curved surface area of the cylinder.
The curved surface area of a right circular cylinder = 2πrh
Diameter of the frame, d = 20 cm
Radius of the frame, r = d/2 = 20/2 cm = 10 cm
Height of the cylinder frame = 30 cm
Here, height will be equal to the height of cylinder plus 2.5 cm margin on both the sides which is used as an extra part for folding.
Height of the lampshade, h = 30 cm + 2.5 cm + 2.5 cm = 35 cm
Thus, cloth required for covering the lampshade = 2πrh
= 2 × 22/7 × 10 cm × 35 cm
= 2200 cm²
Thus, the area of the cloth required is 2200 cm².
☛ Check: NCERT Solutions for Class 9 Maths Chapter 13
Video Solution:
In Fig. 13.12, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.2 Question 10
Summary:
It is given that the frame of a lampshade is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm with a margin of 2.5 cm given for folding it over the top and bottom of the frame.We have found that the area of cloth required to cover the frame is 2200 cm².
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