Question

a cylindrical tub of radius 7cm and length 10.5cm is full of water. A soild in the form of right circular cone mounted on a hemisphere is immersed into the tub. The radius of hemisphere is 3.5cm and height of cone outside the hemisphere is 7cm Find the volume of water left in the tub​

Answer 1

Answer:

Given, radius of the hemisphere,r=3.5cm

Now, since the solid is in the form of a right circular cone mounted on a hemisphere,

then radius of base of the cone=radius of the hemisphere

⇒ radius of the base of the cone=r=3.5cm

Height of the cone,h=4cm

So,

volume of the solid=volume of the cone+ volume of the hemisphere

⇒ volume of the solid=

3

1

πr

2

h+

3

2

πr

3

⇒ volume of the solid=

3

1

πr

2

(h+2r)

⇒ volume of the solid=

3

1

×

7

22

×(4+7)=141.16cm

3

Now, radius of the base of the cylindrical vessel,r

1

=5cm

Height of the cylindrical vessel,h

1

=10.5cm

∴ Volume of the water in the cylindrical vessel==πr

1

2

h

1

=

7

22

×25×10.5=825cm

3

Now, when the solid is completely submerged in the cylindrical vessel full of water, then

volume of the water displaced by the solid= volume of solid

Hence, volume of the water left in the vessel= volume of the water in the vessel- volume of solid

=(825−141.16)cm

3

=683.84cm

3

.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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