# CURVED SURFACE AREA AND TOTAL SURFACE AREA OF SPHERE AND HEMISPHERE

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.

## Formula for Curved Surface Area and Total Surface Area of Hemisphere  Curved surface area  =  2Πr2Hollow hemisphere= 2Π(R2 + r2) sq. unitsTotal surface area of =  3Πr2Hollow hemisphere =  Π(3R2 + r2) sq. units

## Curved Surface Area and Total Surface Area of hemisphere - Examples

Question 1 :

The radius of a sphere increases by 25%. Find the percentage increase in its surface area.

Solution :

Increased percentage of radius  =  125% of r

=  125r/100

=  5r/4

Surface area of hemisphere   =  2Πr2

Surface area of increased hemisphere   =  2Π(5r/4)2

=  25Πr2/8

=  [(25Πr2/8) - (2Πr2)]/(2Πr2)

=  9Πr2/8(2Πr2)

=  9Πr2/16 Πr2

=  0.5625

=  0.5625 (100)

=  56.25%

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

Solution :

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)

=  1860.57

Cost of painting  =  0.14 per cm2

Required cost  =  0.14 (1860.57)

=  260.48

## Curved Surface Area and Total Surface Area of Frustum Cone C.S.A. of a frustum  =  Π(R +r)l sq. unitsT.S.A. of a frustum  =  Π(R + r)l + Π(R2+ r2)where, l = √[h2 +(R −r)2]

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. Solution :

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]

=  (22/7)[180+36]

=  678.85

Cost per sq.cm is 2

Required cost  =  678.85 (2)

=  1357.71 After having gone through the stuff given above, we hope that the students would have understood, "Curved Surface Area and Total Surface Area of Sphere and Hemisphere".

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