A vessel is a hollow cylinder fitted with hemispherical bottom of the same base. The depth of cylinder is 4 2 3 m and the diameter of the hemisphere is 3 . 5 m . Calculate the volume and the internal surface area of the hollow cylinder.

Radius of hemispherical/cylindrical part of vessel r = diameter 2 = 3 . 5 2 = 7 4 m Height of cylinder h = 4 2 3 m = 14 3 m Volume of vessel = Volume of cylindrical part + Volume of hemispherical part = πr 2 h + 2 3 πr 3 = πr 2 h + 2 3 r = 22 7 × 7 4 2 × 14 3 + 2 3 × 7 4 = 22 × 7 16 × 14 3 + 7 6 = 22 × 7 16 × 35 6 = 5390 96 = 56 . 15 m 3 Internal SA of vessel = CSA of cylinder + CSA of hemisphere = 2 πrh + 2 πr 2 = 2 πr h + r = 2 × 22 7 × 7 4 × 14 3 + 7 4 = 11 × 56 + 21 12 = 11 × 77 12 = 847 12 = 70 7 12 m 2 Thus, the volume and internal surface area of the hollow cylinder are 56 . 15 m 3 and 70 7 12 m 2 respectively.

A vessel is a hollow cylinder fitted with hemispherical bottom of the same base. The depth of cylinder is 4 2 3 m and the diameter of the hemisphere is 3 . 5 m . Calculate the volume and the internal surface area of the hollow cylinder.

Radius of hemispherical/cylindrical part of vessel r = diameter 2 = 3 . 5 2 = 7 4 m Height of cylinder h = 4 2 3 m = 14 3 m Volume of vessel = Volume of cylindrical part + Volume of hemispherical part = πr 2 h + 2 3 πr 3 = πr 2 h + 2 3 r = 22 7 × 7 4 2 × 14 3 + 2 3 × 7 4 = 22 × 7 16 × 14 3 + 7 6 = 22 × 7 16 × 35 6 = 5390 96 = 56 . 15 m 3 Internal SA of vessel = CSA of cylinder + CSA of hemisphere = 2 πrh + 2 πr 2 = 2 πr h + r = 2 × 22 7 × 7 4 × 14 3 + 7 4 = 11 × 56 + 21 12 = 11 × 77 12 = 847 12 = 70 7 12 m 2 Thus, the volume and internal surface area of the hollow cylinder are 56 . 15 m 3 and 70 7 12 m 2 respectively.

MEDIUM

10th CBSE

IMPORTANT

Earn 100

A vessel is a hollow cylinder fitted with hemispherical bottom of the same base. The depth of cylinder is $4 \frac{2}{3} m$ and the diameter of the hemisphere is $3.5 m$ . Calculate the volume and the internal surface area of the hollow cylinder.

Important Questions on Surface Areas & Volumes

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 4

Karthik, an engineering student is asked to make a model in his workshop, which is shaped like a cylinder with two equal cones attached at the two ends, the diameter of the model is

3.5 cm

and the length is

18 cm

. If each cone has a height of

4 cm

, if the volume of the model that Karthik made is

k {cm}^{3}

then find

k

. Write the answer upto two decimal places.

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 5

A blacksmith, Sujan made a pillar which consists of a cylindrical portion

2.8 m

high and

20 cm

in diameter and a cone

4.2 cm

high is surmounting it. Find the weight of the pillar(in kgs), if

1 {cm}^{3}

of iron weighs

7.5 grams

.(Write the final answer in decimals without units)

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 6

A rocket which was prepared is in the form of a cylinder closed at the lower end with a cone of the same base radius attached to the top. The cylinder is of radius

2.5 m

and height

21 m

and the cone has the slant height

8 m

.If the volume of the rocket is

a m^{3}

, find the value of

a

. Write the answer upto two decimal places

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 7

An iron pillar has some part in the form of a right circular cylinder and the remaining in the form of a right circular cone. The radius of the base of cylinder and cone is

8 cm

. The cylindrical part is

240 cm

high and conical part is

36 cm

high. If the weight of the pillar is

W kg

, where one cubic cm of iron weighs

7.8

grams, then find the value of

W

(Write the answer up to two decimal places).

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 9

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. Height of the cone is $2 cm$ and the diameter of base is $4 cm$ . If a right circular cylinder circumscribes the toy, if $k π c m^{3}$ more space will it cover? Find $k$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 10

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is

4.2 cm

and the total height of the toy is

10.2 cm

, find the volume of the wooden toy.

[Take, π = \frac{22}{7}]

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 11

A cylindrical container is filled with ice cream whose diameter is

12 cm

and height is

15 cm

. The whole ice-cream is distributed to

10

children in equal cones filled making hemispherical tops. If the height of conical portion is twice than the diameter of its base, find the diameter of the ice-cream cone.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 13 - Surface Areas & Volumes>EXERCISE>Q 12

Building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41 \frac{19}{21} m^{3}$ of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building. [Take $π = \frac{22}{7}$ ]

A vessel is a hollow cylinder fitted with hemispherical bottom of the same base. The depth of cylinder is 423 m and the diameter of the hemisphere is 3.5 m. Calculate the volume and the internal surface area of the hollow cylinder.

Important Questions on Surface Areas & Volumes

Learn and Prepare for any exam you want !

A vessel is a hollow cylinder fitted with hemispherical bottom of the same base. The depth of cylinder is $4 \frac{2}{3} m$ and the diameter of the hemisphere is $3.5 m$ . Calculate the volume and the internal surface area of the hollow cylinder.