NCERT Solution: Surface Areas and Volumes
Given; volume = 48 π cubic cm, h = 9 cm, r = ?
Volume of cone = 1/3 π r2 h
Or, 48 π = 1/3 π r2 X 9
Or, r2 = 48/3 = 16
Or, r = 4 cm
Given; r = 3.5 m, h = 12 m
Volume of cone = 1/3 π r2 h
= (1/3) X (22/7) X (3.5)2 X 12 = 154 cubic cm
= 154 kilo litre
Given; volume = 9856 cubic cm, d = 28 cm so, r = 14 cm
Volume of cone = 1/3 π r2 h
Or, 9856 = (1/3) X (22/7) X 142 X h
Or, h = (9856 X 3 X 7)/(22 X 196) = 48 cm
Slant Height:
Here; l2 = h2 + r2
= 482 + 142 = 2500
Or, l = 50 cm
Curved surface area of cone = π rl
= (22/7) X 14 X 50 = 2200 sq cm
Given; h = 12 cm, r = 5 cm
Volume of cone = 1/3 π r2 h
= (1/3) π X 52 X 12 = 100 π cubic cm
Given; h = 5 cm, r = 12 cm
Volume of cone = 1/3 π r2 h
= (1/3) π X 122 X 5 = 240 π cubic cm
Ratio = 100/240 = 5 : 12
Given; r = 5.25 m, h = 3 m
Volume of cone = 1/3 π r2h
= (1/3) X (22/7) X (5.25) X 3
= 50.625 cubic m
(i) 7 cm
Solution: Volume of sphere = 4/3 π r2
= (4/3) X (22/7) X 73 = 1437.33 cubic cm
(ii) 0.63 m
Solution: Volume of sphere = 4/3 π r3
= (4/3) X (22/7) X (0.63)3 = 1.047 cubic m
(i) 28 cm
Solution: Volume of sphere = 4/3 π r3
= (4/3) X (22/7) X 283 = 91989.33 cubic cm
(ii) 0.21 m
Solution: Volume of sphere = 4/3 π r3
= (4/3) X (22/7) X (0.21)3 = 0.38808 cubic m