PROBLEMS ON SURFACE AREA OF SPHERE AND HEMISPHERE

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

⋅ (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

r2  =  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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