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SURFACE AREAS

AND VOLUMES

  • Sum based on Cylinder, Hemisphere and Cone (Part II)

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Q. A toy is combination of a cylinder, hemisphere and a cone,

each with radius 10 cm. Height of the conical part is 10 cm and total

height is 60 cm. Find the total surface area and volume of the toy.

× 10

Volume of toy

= Volume of cone

+ Volume of cylinder

+ Volume of hemisphere

10 cm

10 cm

10 cm

Volume of toy =

3.14 ×

10 × 10

l = 14.1cm

1

3

πr2h

=

+

πr2H

+

2

3

πr3

=

πr2

× h +

1

3

H +

2

3

× r

=

1

3

+ 40

+

2

3

× 10

What is formula for finding volume of hemisphere ?

What is formula for finding volume of cylinder ?

40 cm

10 cm

What is formula for finding volume of cone ?

Volume of cone +

Volume of hemisphere

Volume of cylinder +

π r2 H

 

 

Sol.

60 cm

×

✔

✔

✔

✔

✔

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Volume of toy =

Volume of cone +

Volume of hemisphere

Volume of cylinder +

10 cm

10 cm

10 cm

60 cm

10 cm

40 cm

Sol.

​

​

Volume of toy is 15700 cm3

∴

314

=

314

=

15700 cm3

=

3.14 ×

10 × 10

=

10

3

+ 40

+

20

3

30

3

+ 40

10

× 10

3.14 ×

10 × 10

=

1

3

+ 40

+

2

3

× 10

×

Q. A toy is combination of a cylinder, hemisphere and a cone,

each with radius 10 cm. Height of the conical part is 10 cm and total

height is 60 cm. Find the total surface area and volume of the toy.

×

×

314 × (10 + 40)

=

× 50