A building is in the form of a cylinder surmounted by a hemisphere valted dome and contains 41 19 21 m 3 of air. If the internal diameter of dome is equal to the total height of the building, find the height of the building.

Let the total height of the building be H m . Let the radius of the base be r m . Therefore the radius of the hemispherical dome is r m . Now given that internal diameter = total height ⇒ 2 r = H Total height of the building = height of the cylinder + radius of the dome ⇒ H = h + r ⇒ 2 r = h + r ⇒ r = h Volume of the air inside the building = volume of the cylinder + volume of the hemisphere ⇒ 41 19 21 = π r 2 h + 2 3 π r 3 ⇒ 880 21 = π h 2 h + 2 3 π h 3 ⇒ 880 21 = π h 3 1 + 2 3 ⇒ 880 21 = π h 3 5 3 ⇒ h = 2 m Height of the building H = 2 × 2 = 4 m Hence, height of the building is 4 m .

A solid metallic sphere of radius 6 c m is melted and made into a solid cylinder of height 32 c m . Find the curved surface area of the cylinder. (Take π = 3 . 1 )

Radius of metallic sphere R = 6 c m Height of cylinder h = 32 c m Volume of cylinder = Volume of metallic sphere π r 2 h = 4 3 π R 3 r 2 × 32 = 4 3 × 6 3 r 2 = 4 × 6 × 6 × 6 3 × 32 r 2 = 9 r = 3 c m Then, curved surface area of the cylinder = 2 π r h = 2 × 3 . 1 × 3 × 32 = 595 . 2 c m 2

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A circus tent is in the shape of cylinder surmounted by a cone. The diameter of the cylindrical portion is $24 m$ and its height is $11 m$ . If the vertex of the cone is $16 m$ above the ground, find the area of the canvas used to make a tent?

Important Questions on Mensuration

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10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 11

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 the 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 folds and stitching. Give your answer nearest

m^{2}

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 12

From a solid cylinder of height

30 cm

and radius

7 cm

, a conical cavity of height

24 cm

and of base radius

7 cm

is drilled out. Find the volume and the total surface of the remaining solid.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 13

The adjoining figure shows a hemisphere of radius $5 cm$ surmounted by a right circular cone of base radius $5 cm$ . Find the volume of the solid if the height of the cone is $7 cm$ . Give your answer correct to two places of decimal.

Question Image

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 14

A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is

3.5

metres and its volume is

\frac{2}{3}

of the hemisphere. Calculate the height of the cone and the surface area of the buoy correct to

2

places of decimal.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 15

A building is in the form of a cylinder surmounted by a hemisphere valted dome and contains

41 \frac{19}{21} m^{3}

of air. If the internal diameter of dome is equal to the total height of the building, find the height of the building.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 16

A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and the height of the cylinder are

6 cm

and

12 cm

respectively. If the slant height of the conical porticn is

5 cm

, find the total surface area and the volume of the rocket.
(Use

π = 3 \cdot 14

)

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 17

The adjoining figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is $7 cm$ . The height of the cylinder and the cone are each of $4 cm$ . Find the volume of the solid.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 18

A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. Their common diameter is

3.5 cm

and the height of the cylindrical and conical portions are

10 cm

and

6 cm

respectively. Find the volume of the solid. (Take

π = 3 \cdot 14

)

A circus tent is in the shape of cylinder surmounted by a cone. The diameter of the cylindrical portion is 24 m and its height is 11 m. If the vertex of the cone is 16 m above the ground, find the area of the canvas used to make a tent?

Important Questions on Mensuration

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A circus tent is in the shape of cylinder surmounted by a cone. The diameter of the cylindrical portion is $24 m$ and its height is $11 m$ . If the vertex of the cone is $16 m$ above the ground, find the area of the canvas used to make a tent?