Surface area and Volume ( Part – 6 )
1. The curved surface area of a right circular cylinder of
height 7 cm is 44 cm^2 . Find the diameter of the base of the cylinder ?
Sol. Curved surface area of cylinder 44 cm^2 and height h =
7 cm
Let , the radius of base of cylinder = r cm
Curved surface area of cylinder = 2 ∏ r h
44 = ( 2 * 22 * r * 7 ) / 7
44 = 44 r
r = 1 cm
Hence , the diameter of base of cylinder = 2 r = 2 * 1 = 2
cm
2. The curved surface area of a right circular cylinder of
height 21 cm is 132 cm^2 . Find the diameter of the base of the cylinder ?
Sol. Curved surface area of cylinder 132 cm^2 and height h =
21 cm
Let , the radius of base of cylinder = r cm
Curved surface area of cylinder = 2 ∏ r h
132 = ( 2 * 22 * r * 21 ) / 7
132 = 132 r
r = 1 cm
Hence , the diameter of base of cylinder = 2 r = 2 * 1 = 2 cm
3. The curved surface area of a right circular cylinder of
height 28 cm is 176 cm^2 . Find the diameter of the base of the cylinder ?
Sol. Curved surface area of cylinder 176 cm^2 and height h =
28 cm
Let , the radius of base of cylinder = r cm
Curved surface area of cylinder = 2 ∏ r h
176 = ( 2 * 22 * r * 28 ) / 7
176 = 176 r
r = 1 cm
Hence , the diameter of base of cylinder = 2 r = 2 * 1 = 2
cm
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4. It is required to make a closed cylindrical tank of
height 1 m and base diameter 70 cm from a metal sheet . How many square meters
of the sheet are required for the same ?
Sol. Radius of base of cylinder r = 70 / 2 = 35 cm = 0.35 m
and height h = 1 m
Total surface area of cylinder = 2 ∏ r ( r + h )
Total surface area of cylinder = ( 2 * 22 * 0.35 ) / 7 * ( 0.35 + 1
)
Total surface area of cylinder = 2.2 * 1.7
Total surface area of cylinder = 3.74 m^2
Hence , 3.74 square meter metal sheet is required to make
the closed cylindrical tank .
5. It is required to make a closed cylindrical tank of
height 1 m and base diameter 210 cm from a metal sheet . How many square meters
of the sheet are required for the same ?
Sol. Radius of base of cylinder r = 210 / 2 = 105 cm = 1.05
m and height h = 1 m
Total surface area of cylinder = 2 ∏ r ( r + h )
Total surface area of cylinder = ( 2 * 22 * 1.05 ) / 7 * ( 1.05 + 1
)
Total surface area of cylinder = 6.6 * 2.05
Total surface area of cylinder = 13.53 m^2
Hence , 13.53 square meter metal sheet is required to make
the closed cylindrical tank .
6. It is required to make a closed cylindrical tank of
height 1 m and base diameter 280 cm from a metal sheet . How many square meters
of the sheet are required for the same ?
Sol. Radius of base of cylinder r = 280 / 2 = 140 cm = 1.40
m and height h = 1 m
Total surface area of cylinder = 2 ∏ r ( r + h )
Total surface area of cylinder = ( 2 * 22 * 1.40 ) / 7 * ( 1.40 + 1
)
Total surface area of cylinder = 61.6 * 2.40
Total surface area of cylinder = 147.84 m^2
Hence , 147.84 square meter metal sheet is required to make
the closed cylindrical tank .
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