A test tube consists of a hemisphere and a cylinder of the same radius. The volume of the water required to fill the whole tube is 5159 6 cm 3 , and 4235 6 cm 3 of water is required to fill the tube to a level which is 4 cm below the top of the tube. Find the radius of the tube and the length of its cylindrical part.

Volume of water filled in test tube = 5159 6 cm 3 volume of water filled upto 4 cm = 4235 6 cm 3 Let r let the radius of tube and h be the height of test tube. ∴ 2 3 π r 3 + π r 2 h = 5159 6 πr 2 2 3 r + h = 5159 6 πr 2 3 2 r + 3 h = 5159 6 ⇒ πr 2 ( 2 r + 3 h ) = 5159 6 . . . . . . . . . . . . . ( i ) and 2 3 πr 3 + πr 2 ( h - 4 ) = 4235 6 ⇒ πr 2 2 3 r + h - 4 = 4235 6 ⇒ πr 2 3 2 r + 3 h - 12 = 4235 6 ⇒ πr 2 ( 2 r + 3 h - 12 ) = 4235 2 . . . . . . . ( ii ) Dividing ( i ) and by ( ii ) 2 r + 3 h 2 r + 3 h - 12 = 5159 4235 . . . . . ( iii ) Subtracting ( ii ) from ( i ) πr 2 ( 12 ) = 5159 2 - 4235 2 = 924 2 ⇒ r 2 = 924 × 7 2 × 12 × 22 = 7 × 7 2 × 2 ⇒ r 2 = 49 4 ⇒ r = 7 2 = 3 . 5 cm Substituting value of r in equation ( iii ) 2 × 7 2 + 3 h 2 × 7 2 + 3 h - 12 = 5159 4235 ⇒ 7 + 3 h 7 + 3 h - 12 = 5159 4235 ⇒ 7 + 3 h 7 + 3 h - 12 = 469 385 ⇒ 2695 + 1155 h = 1407 h - 2345 ⇒ 252 h = 5040 ⇒ h = 20

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The given figure shows the crosi-section of a cone, a cylinder and a hemisphere all with the same diameter $10 cm,$ and the other dimensions are as shown.
Calculate the total volume of the solid and

Important Questions on Cylinder, Cone and Sphere (Surface Area and Volume)

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 12

The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter $10 cm,$ and the other dimensions are as shown.
Calculate:
Question Image

The density of the material if its total weight is $1.7 kg .$

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 13

A solid, consisting of a right circular cone standing on a hemisphere, is placed upright in a right circular cylinder, full of water, and
touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is

3 cm

and its height is

6 cm;

the radius of the hemisphere is

2 cm

and the height of cone is

4 cm .

Give your answer to the nearest cubic centimetre.

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 14

A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is

7 m

and the internal radius is

3 - 5 m .

Calculate the total area of the internal surface, excluding the base.

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 14

A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is $7 m$ and the intemal radius is $3.5 m$ Calculate:
the internal volume of the container in $m^{3} .$

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 15

An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is

85 m

and height of the cylindrical part is

50 m .

If the diameter of the base is

168 m,

find the quantity of canvas required to make the tent. Allow

20 %

extra for fold and for stitching. Give your answer to the nearest

m^{2} .

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 16

A test tube consists of a hemisphere and a cylinder of the same radius. The volume of the water required to fill the whole tube is $\frac{5159}{6} {cm}^{3},$ and $\frac{4235}{6} {cm}^{3}$ of water is required to fill the tube to a level which is $4 cm$ below the top of the tube. Find the radius of the tube and the length of its cylindrical part.

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 17

A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with
hemisphere, is

7 cm

and its height is

8 cm .

The solid is placed in a cylindrical vessel of internal radius

7 cm

and height

10 cm .

How much water, in

{cm}^{3},

will be required to fill the vessel completely

?

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Concise Mathematics>Chapter 20 - Cylinder, Cone and Sphere (Surface Area and Volume)>EXERCISE>Q 18

Two solid spheres of radii

2 cm

and

4 cm

are melted and recast into a cone of height

8 cm .

Find the radius of the cone so formed.

The given figure shows the crosi-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm, and the other dimensions are as shown. Calculate the total volume of the solid and

Important Questions on Cylinder, Cone and Sphere (Surface Area and Volume)

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The given figure shows the crosi-section of a cone, a cylinder and a hemisphere all with the same diameter $10 cm,$ and the other dimensions are as shown.
Calculate the total volume of the solid and