[10/12, 8:58 PM] Chulu: Ex 13.1 Class 9 Maths Question 1. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine (i) The area of the sheet required for making the box. (ii) The cost of sheet for it, if a sheet measuring 1m2 costs ₹20. Solution: (i) Here, length (l) = 1.5 m, bread th(b) = 1 .25 m and height (h) = 65 cm = 65100 m = 0.65 m NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.1 Q1 ∵ It is open from the top. ∴ Its surface area = [Lateral surface area] + [Base area] = [2(1 + b)h] + [lb] = [2(1.50 + 1.25)0.65] m2 + [1.50 x 1.25] m2 = [2 x 2.75 x 0.65] m2 + [1.875] m2 = 3.575 m2+ 1.875 m2 = 5.45 m2 ∴ Area of the sheet required for making the box = 5.45 m2 (ii) Cost of 1 m2 sheet = Rs. 20 Cost of 5.45 m2 sheet = Rs. (20 x 5.45) = Rs. 109 Hence, cost of the required sheet = Rs. 109 [10/12, 8:59 PM] Chulu: Ex 13.1 Class 9 Maths Question 2. The length, breadth and height of a room are 5 m, 4 m and 3 m, respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of ₹17.50 per m2. Solution: Length of the room (l) = 5 m Breadth of the room (b) = 4 m Height of the room (h) = 3 m The room is like a cuboid whose four walls (lateral surface) and ceiling are to be white washed. ∴ Area for white washing = [Lateral surface area] + [Area of the ceiling] = [2(l + b)h] + [l x b] = [2(5 + 4) x 3] m2 + [5 x 4] m2 = 54 m2 + 20 m2 = 74 m2 Cost of white washing for 1 m2 area = Rs. 7.50 ∴ Cost of white washing for 74 m2 area = Rs. (7.50 x 74) = Rs. 555 Thus, the required cost of white washing = Rs. 555
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[10/12, 8:58 PM] Chulu: Ex 13.1 Class 9 Maths Question 1.
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1m2 costs ₹20.
Solution:
(i) Here, length (l) = 1.5 m, bread th(b) = 1 .25 m
and height (h) = 65 cm = 65100 m = 0.65 m
NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.1 Q1
∵ It is open from the top.
∴ Its surface area
= [Lateral surface area] + [Base area]
= [2(1 + b)h] + [lb]
= [2(1.50 + 1.25)0.65] m2 + [1.50 x 1.25] m2
= [2 x 2.75 x 0.65] m2 + [1.875] m2
= 3.575 m2+ 1.875 m2 = 5.45 m2
∴ Area of the sheet required for making the box = 5.45 m2
(ii) Cost of 1 m2 sheet = Rs. 20
Cost of 5.45 m2 sheet = Rs. (20 x 5.45)
= Rs. 109
Hence, cost of the required sheet = Rs. 109
[10/12, 8:59 PM] Chulu: Ex 13.1 Class 9 Maths Question 2.
The length, breadth and height of a room are 5 m, 4 m and 3 m, respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of ₹17.50 per m2.
Solution:
Length of the room (l) = 5 m
Breadth of the room (b) = 4 m
Height of the room (h) = 3 m
The room is like a cuboid whose four walls (lateral surface) and ceiling are to be white washed.
∴ Area for white washing
= [Lateral surface area] + [Area of the ceiling]
= [2(l + b)h] + [l x b]
= [2(5 + 4) x 3] m2 + [5 x 4] m2 = 54 m2 + 20 m2 = 74 m2
Cost of white washing for 1 m2 area = Rs. 7.50
∴ Cost of white washing for 74 m2 area = Rs. (7.50 x 74) = Rs. 555
Thus, the required cost of white washing = Rs. 555
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