Problem 1 :
If the curved surface area of solid sphere is 98.56 cm2, then find the radius of the sphere.
Solution :
Curved surface area of sphere = 98.56 cm2
4 Π r2 = 98.56
4 ⋅ (22/7) ⋅ r² = 98.56
r2 = 98.56 ⋅ (1/4) ⋅ (7/22)
r2 = 98.56 ⋅ (1/4) ⋅ (7/22)
r2 = 7.84
r = √(2.8 ⋅ 2.8)
r = 2.8 cm
So, radius of the sphere is 2.8 cm.
Problem 2 :
If the curved surface area of the solid hemisphere is 2772 sq.cm, then find its total surface area.
Solution :
Curved surface area of hemisphere = 2772 cm2
2Πr2 = 2772
2 ⋅ (22/7) ⋅ r2 = 2772
r2 = 2772 ⋅ (1/2) ⋅ (7/22)
r2 = 441
r = 21
Total surface area of hemisphere = 3Πr2
= 3 ⋅ (22/7) ⋅(21)2
= 4158 cm2
Total surface area of sphere = 4158 cm²
Problem 3 :
Radii of two solid hemispheres are in the ratio 3:5. Find the ratio of their curved surface areas and the ratio of their total surface areas.
Solution :
Let r₁ and r₂ are the radii of two hemispheres
r1 : r2 = 3:5
r1 / r2 = 3/5
r1 = 3r2/5
Curved surface area of hemisphere = 2Πr2
Ratio of curved surface area of two hemisphere
2 Π r2 : 2 Π r2
(3 r2/5)2 : r22
9 : 25
Total surface area of hemisphere = 3Πr²
Ratio of curved surface area of two hemisphere
3Π r12 : 3 Πr22
(3 r₂/5)² : r₂²
9 : 25
Ratio of curved surface area is 9 : 25
Ratio of total surface area is 9 : 25
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