Page 245 - ICSE Math 8

Example 19: A rectangular sheet of aluminium foil is 44 cm long and 22 cm wide. A cylinder is made out
it by rolling the foil along its length. Find the total surface area of the cylinder.
Solution: Height of cylinder (h) = 22 cm
Let the radius of cylinder be r cm.
22 cm
Circumference of base of cylinder = 44 cm
(  Length of rectangle becomes the circumference of base) 44 cm

22
fi 2pr = 44 fi 2 × × r = 44
7 r
744¥
fi r = = 7 cm
222¥ h 22 cm

Hence, radius of base (r) = 7 cm
22
\ Total surface area = 2pr(h + r) = 2 × × 7 × (22 + 7) cm 2
7
22
2
= 2 × × 7 × 29 cm = 1,276 cm 2
7
Example 20: An open cylindrical tank of depth 1.5 m and radius of base 70 cm is to be made from a metal
sheet. How many square metres of metal sheet is needed?

Solution: Height of cylinder (h) = 1.5 m, Radius of base (r) = 70 cm = 0.7 m
Since the cylinder is open from the top,
the area of metal sheet needed = CSA + Area of base

= 2prh + pr 2
22 22
= 2 × × 0.7 × 1.5 + × 0.7 × 0.7
7 7
2
= (6.6 + 1.54) m = 8.14 m 2
2
Hence, 8.14 m of metal sheet is required to make the cylindrical tank.
2
Example 21: The lateral surface area of a hollow cylinder is 4,224 cm . It is cut along its height and
formed into a rectangular sheet of width 33 cm. Find the perimeter of the rectangular
sheet.
Solution: Let the height of cylinder (h) = width of the sheet (b) = 33 cm and the radius of the base of
hollow cylinder be r cm.
\ Length of sheet = Circumference of base = 2pr cm

Also, lateral surface area = 2prh 33 cm
fi 4,224 = 2pr × 33

4 224,
fi 2pr = = 128
33
\ Length of sheet (l) = 128 cm 33 cm
Perimeter of sheet = 2(l + b) = 2(128 + 33) cm

= 2 × 161 cm = 322 cm 2pr cm
\ Perimeter of rectangular sheet = 322 cm

233