DIFFERENT TYPES OF SHAPES

•CUBOID• CUBE

• SPHERE

• HEMISPHERE

• CYLINDER

•CONE

When a plane through the centre of a sphere cuts it into two equal parts is called a

hemisphere.

FORMULAE’S

EXAMPLE -1A hemispherical dome of a building needs to be painted. If the circumference of the base

of the dome 15.8,find the cost of painting it,given the cost of painting Rs. 10per

100cm.square.

SOLUTON-1

2x22/7x79/10x79/102

= 392.30 (cm ) =3920.30=Rs.1,96,150 (Ans)

EXAMPLE-2

The circumference of the edge of a hemispherical bowl is 132cm.Find the capacity of the bowl.

SOLUTION-2 Circumference = 2 r

132 =2x22/7xrR= 132x7/2x22

R=21

Capacity=

2/3x22/7x21x21x213

= 19404 cm (Ans)

EXAMPLE-3

Find the volume ,curved surface area and the total surface area of hemisphere of diameter 7 cm?

SOLUTION -3

) =2 x14x14cm.square =(392 )cm.square =2/3x22/7x7/2x7/2x7/2 cm.cube

2x22/7x2/7/2 =77cm.square

539/6 = 89.83cm.cube

3x22/7x7/2x7/2 =115.5cm.square. (Ans)

• A hemisphrical bowl is made up of steel,0.75m

thick.The inner radius of the bowl is 15m . Find the outer curved surface area ?

• R = thickness + inner radius• = 0.75 + 15 = 15.75

= 2x22/7x15.75x15.75 = 1559.25m.square.

EXAMPLE-5• The volume of hemisphere is 5544cm.square. Find its radius ?

SOLUTION -5

• 3• 5544 = 2/3x22/7x r • 3• 5544x7/2x22= r• cube root of r =756 • r = 19.63cm.cube.

EXAMPLE- 6• If diameter of a solid hemisphere is half then

its total surface area ill be decreased by 75%.

SOLUTION - 6• Let diameter be = x• Radius = x/2

• 3 (x/4) = 3 r.square./16• change in T.S.A original-new/originalx100• 3 r.square / 4 -3 r.square /16 x 100 • 4

• 12 r.square – 3 r.square/16/3 r square/4

• 9 x.square/16/3 r.square/4• 3/4x100• = 3x25• = 75% (Ans)

QUESTION - 1 & 2• Find the volume of hemisphere whose radius

is 21 cm ? • ANS. 19404 cm.cube

Find the total surface area and the curved surface area whose radius is 7 cm?

ANS. 462 cm. square 308 cm .square

THANKYOU