The sum of the area of two ends of a right circular cylinder is equal to 1 3 of its curved surface. Find ratio of the height and diameter of the cylinder.

Let the height of the right circular cylinder be H and the diameter of the right circular cylinder be R . Radius of the right circular cylinder = R 2 Sum of area of two ends of the right circular cylinder = π R 2 2 + π R 2 2 = 2 π R 2 4 = π R 2 2 Area of the curved surface of the right circular cylinder = 2 π H × R 2 = π H R Given, the sum of the area of two ends of a right circular cylinder is equal to 1 3 of its curved surface. Therefore, π R 2 2 = 1 3 × π R H ⇒ R 2 = H 3 ⇒ H R = 3 2 ⇒ H : R = 3 : 2 Hence, the ratio of the height and diameter of the cylinder is 3 : 2 .

HARD

10th West Bengal Board

IMPORTANT

Earn 100

In a right-angled triangle, the length of the sides containing the right angle are $12 c m$ and $35 c m$ . Find the volume of the cone formed by rotating the triangle considering the greater side as its axis.

Important Questions on Miscellaneous Exercise : Mensuration

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 1

The diameter of base of a right circular cone is equal to the radius of the sphere. If the volume of the cone and the sphere are equal, then what is the ratio of the height and diameter of the cone?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 2

The height of a right circular cylinder is

15 cm

and the area of lateral surface is

660 {cm}^{2}

. What is the diameter of the cylinder?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 2

The sum of the area of two ends of a right circular cylinder is equal to

\frac{1}{3}

of its curved surface. Find ratio of the height and diameter of the cylinder.

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 2

The area of curved surface of a right circular cylinder is

100 π {cm}^{2}

and its height is equal to the diameter of the base. What is the height of the cylinder?

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 3

The height and the diameter of a right circular cylinder are equal. What is the ratio of the total surface area and the curved surface area?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 3

The inner radius of a cylinder, open at one end is

3 m

and length is

8 m

. What is the maximum length of a rod that can be put in the cylinder?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 4

If the ratio of the radius of two right circular cylinders of same height is

3 : 4

, then what will be the ratio of their volumes?

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 31 - Miscellaneous Exercise : Mensuration>Miscellaneous Exercise : Mensuration>Q 4

The diameter of a thin copper wire is

1 cm

and length

14 m

. What is the amount of copper in the wire?

In a right-angled triangle, the length of the sides containing the right angle are 12 cm and 35 cm. Find the volume of the cone formed by rotating the triangle considering the greater side as its axis.

Important Questions on Miscellaneous Exercise : Mensuration

Learn and Prepare for any exam you want !

In a right-angled triangle, the length of the sides containing the right angle are $12 c m$ and $35 c m$ . Find the volume of the cone formed by rotating the triangle considering the greater side as its axis.