SURFACE AREAS

AND VOLUMES

• Sum based on Cylinder and Cuboid

17. Rohan’s house has an overhead tank in the shape of a cylinder.

This is filled by pumping water from an underground tank which is in the shape of a cuboid.

The underground tank has dimensions 1.5m × 1.44m × 95cm. The overhead tank has its

radius 60 cm and height 95 cm. Find the height of the water left in the underground tank

after the overhead tank has been completely filled with water from underground tank which

had been full. Compare the capacity of both the tanks. (Take  = 3.14 )

Vol. of water left in

the underground tank

=

Vol. of water in

the overhead tank

Vol. of water in the underground tank

–

H = ?

17. Rohan’s house has an overhead tank in the shape of a cylinder.

This is filled by pumping water from an underground tank which is in the shape of a cuboid.

The underground tank has dimensions 1.5m × 1.44m × 95cm. The overhead tank has its

radius 60 cm and height 95 cm. Find the height of the water left in the underground tank

after the overhead tank has been completely filled with water from underground tank which

had been full. Compare the capacity of both the tanks. (Take  = 3.14 )

Sol.

Vol. of water left in

the underground tank

=

Vol. of water in

the underground tank

–

Vol. of water in

the overhead tank

l

×

b

×

h

=

–

π r² h₁

l

×

b

×

H

∴

150 cm

150

144 cm

×

144

×

H

=

150

×

144

×

95

–

3.14

×

60

×

60

×

95

=

150

×

36

×

4

×

95

–

×

60

×

60

×

95

=

150

×

36

×

4

×

95

–

314

×

36

×

95

=

36

×

95

×

(150

×

4

–

314)

150

×

144

×

H

150

×

144

×

H

150

×

144

×

H

∴

∴

∴

∴

What is the formula to find

Volume of cuboid?

l × b × h

What is the formula to find

Volume of cylinder?

π r² h

Vol. of water left in

the underground tank

=

Vol. of water in

the overhead tank

Vol. of water in the underground tank

–

150 cm

144 cm

95 cm

=

36

×

95

×

(150

×

4

–

314)

150

×

144

×

H

17. Rohan’s house has an overhead tank in the shape of a cylinder.

This is filled by pumping water from an underground tank which is in the shape of a cuboid.

The underground tank has dimensions 1.5m × 1.44m × 95cm. The overhead tank has its

radius 60 cm and height 95 cm. Find the height of the water left in the underground tank

after the overhead tank has been completely filled with water from underground tank which

had been full. Compare the capacity of both the tanks. (Take  = 3.14 )

Sol.

=

H

95

×

36

×

286

150

×

144

30

19

4

2

143

=

19

×

143

=

36

×

95

×

(600

150

×

144

×

H

–

314)

30

×

2

=

2717

6

×

10

=

452.83

10

H

∴

=

36

×

95

×

286

150

×

144

×

H

∴

∴

∴

H

∴

H

∴

=

45.28 cm

Height of the water left in the underground tank is 45.28 cm

∴

17. Rohan’s house has an overhead tank in the shape of a cylinder.

This is filled by pumping water from an underground tank which is in the shape of a cuboid.

The underground tank has dimensions 1.5m × 1.44m × 95cm. The overhead tank has its

radius 60 cm and height 95 cm. Find the height of the water left in the underground tank

after the overhead tank has been completely filled with water from underground tank which

had been full. Compare the capacity of both the tanks. (Take  = 3.14 )

Sol.

=

l × b × h

Volume of underground tank

150 cm

144 cm

95 cm

150

×

144

×

95

=

cm³

=

πr²h

Volume of overhead tank

3.14

=

× 60

× 60

× 95

=

× 60

× 60

× 95

314

=

× 6

× 6

× 95

cm³

Volume of underground tank

Volume of overhead tank

=

150

×

144

×

95

314

× 6

× 6

× 95

i.e. we have compare the volumes of underground tank and over head tank

Let us calculate volume of underground tank

What is the formula of a cuboid ?

l × b × h

Let us calculate volume of overhead tank

What is the formula of a cylinder ?

πr²h

Let us compare their volumes

17. Rohan’s house has an overhead tank in the shape of a cylinder.

This is filled by pumping water from an underground tank which is in the shape of a cuboid.

The underground tank has dimensions 1.5m × 1.44m × 95cm. The overhead tank has its

radius 60 cm and height 95 cm. Find the height of the water left in the underground tank

after the overhead tank has been completely filled with water from underground tank which

had been full. Compare the capacity of both the tanks. (Take  = 3.14 )

Sol.

Volume of underground tank

Volume of overhead tank

=

150

×

144

×

95

314

× 6

× 6

× 95

24

4

2

157

=

300

157

=

1.91

≅

2

Volume of underground tank

Volume of overhead tank

Volume of underground tank

Volume of overhead tank

≅

2

Volume of underground tank

× Volume of overhead tank

Capacity of underground tank is twice of capacity of overhead tank

∴