Curved Surface Area and Total Surface Area of Sphere and Hemisphere :
Here we are going to see, some example problems of finding curved surface area and total surface area of sphere.
Question 1 :
The radius of a sphere increases by 25%. Find the percentage increase in its surface area.
Radius of hemisphere = r
Increased percentage of radius = 125% of r
Surface area of hemisphere = 2Πr2
Surface area of increased hemisphere = 2Π(5r/4)2
= [(25Πr2/8) - (2Πr2)]/(2Πr2)
= 9Πr2/16 Πr2
= 0.5625 (100)
Question 2 :
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹0.14 per cm2
internal radius (r) = 20/2 = 10 cm
External radius (R) = 28/2 = 14 cm
Curved surface area of hemisphere = 2Π(R2 + r2)
= 2 (22/7)(142 + 102)
= 2 (22/7)(196 + 100)
Cost of painting = ₹0.14 per cm2
Required cost = 0.14 (1860.57)
Question 3 :
Th e frustum shaped outer portion of the table lamp has to be painted including the top part. Find the total cost of painting the lamp if the cost of painting 1 sq.cm is ₹2.
Curved surface area of lamp = Π(R +r)l sq. units
R = 12 m, r = 6 m and h = 8 m
l = √[h2 +(R −r)2]
l = √[82 +(12 −6)2]
l = √[64 + 62]
l = √(64 + 36) = √100
l = 10
C.S.A of frustum shaped lamp = Π(R +r)l
Area to be painted = Π(R +r)l + Πr2
= (22/7)[(12 + 6)(10) + 62]
Cost per sq.cm is ₹2
Required cost = 678.85 (2)
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