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

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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