Right Circular Cone

Q. Question 1
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Q.

A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

1. False

2. True

Q.

If the height and the radius of a cone are doubled, the volume of the cone becomes:

1. $4$ times

2. $3$ times

3. $6$ times

4. $8$ times

Q. Question 4
The shape of a glass ( tumbler) ( see figure) is usually in the form of

(A) a cone
(B) frustum of a cone
(C) a cylinder
(D) a sphere

Q.

If a right angled triangle is revolved about one of the sides containing the right angle it forms a

1. Prism

2. Right circular cone

3. Right triangle

4. Pyramid

Q.

In the figure, Each cube has a volume of 1 cubic unit. Find the volume of the figure and the area of its base.

Q.

Pavan drew a $△$ABC right angled at B. He says if the right angle triangle is rotated along AB then it will result in ___

1. Cuboid
2. Cylinder

3. Cone

4. Cube

Q. A right angle triangle of base 4 cm and height 3 cm is rotated about its height. Then, find the CSA and volume of the solid obtained.

Q. If the slant height of a cone is 5 cm, and its radius is 4 cm, find its height.

1. 3 cm
2. 6 cm
3. 9 cm
4. 12 cm

Q. The central angle and radius of a sector of a circular disc are ${180}^o$ and $21cm$ respectively. If the edges of the sector are joined together to make a hollow cone, then find the radius of the cone.

1. $10.5cm$
2. None of these
3. $10cm$
4. $12.5cm$

Q. If the height and radius of a right circular cone are 'h' and 'r', respectively, then the slant height is equal to $\sqrt{h^2+r^2}$.

1. True
2. False

Q.

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

1. 50 $c{m}^3$

2. 66 $c{m}^3$

3. 62 $c{m}^3$

4. 75 $c{m}^3$

Q.

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

1. 66 $c{m}^3$

2. 62 $c{m}^3$

3. 75 $c{m}^3$

4. 50 $c{m}^3$

Q.

Question 6
A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

Q.

why is it called "right circular cone" and "right circular cylinder" ?

Q.

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

1. 62 $c{m}^3$

2. 50 $c{m}^3$

3. 66 $c{m}^3$

4. 75 $c{m}^3$

Q. The base of a right circular cone is ________ .

1. a circle
2. a rectangle
3. a triangle
4. a square

Q. The base of a right circular cone is ________ .

1. a circle
2. a triangle
3. a square
4. a rectangle

Q. The central angle and radius of a sector of a circular disc are ${180}^o$ and $21$ cm respectively. If the edges of the sector are joined together to make a hollow cone, then find the radius of the cone.

Q.

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

1. 50 $c{m}^3$

2. 66 $c{m}^3$

3. 62 $c{m}^3$

4. 75 $c{m}^3$

Q.

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made . (Assume the outer and inner dimensions of the model to be nearly the same.)

1. 50 $c{m}^3$

2. 62 $c{m}^3$

3. 66 $c{m}^3$

4. 75 $c{m}^3$