Volume of a right circular cone

Q.

Find the volume (in $c{m}^3$ ) of :

1. 58

2. 56.55

3. 50

4. 53.55

Q.

Find the side of a cube whose surface area is 600 $c{m}^2$.

A) 10 cm B) $\sqrt{150}$ cm
C) 100 cm D) $\sqrt{600}$ cm

Q.

An ice-cream machine has two taps for filling ice-cream cones of height 6 cm and radius 3 cm. If the flow rate of ice-cream from both taps is equal to 2 $c{m}^3{s}^{-1}$. Find the maximum number of cones machine can fill in an hour.

1. 248

2. 255

3. 258

4. 260

Q. Find the volume of conical shaped dispenser of height 8 in and radius 2 in as shown in the figure below.

1. 11.1 cu in
2. 16.7 cu in
3. 25.6 cu in
4. 33.5 cu in

Q. The radius of the base of a cylinder is 7 cm and its height is 10 cm. A cone with the same radius as that of the base of the cylinder and a height of 6 cm is placed on the cylinder. What is the volume of the solid formed?

Q.

A right angle triangle of base 4 cm and height 3 cm is rotated about its height. The curved surface area and volume of the solid obtained are _____ ($inc{m}^2$) and _____ ($inc{m}^3$) respectively.

1. $18\pi \&14\pi$
2. $20\pi \&16\pi$
3. $16\pi \&18\pi$
4. $22\pi \&20\pi$

Q.

The height and radius of a cone is 6 cm and 3 cm respectively .The volume of cone is equal to___$\pi {cm}^3$.

Q. The total surface area of a right circular cone of slant height $20cm$ is $384\pi c{m}^2$.
Calculate: (i) its radius in $cm$;
(ii) its volume in $c{m}^3$, in terms of $\pi$.

Q.

The volume of a cone of radius 7 $cm$ and slant height 14 $cm$ is ______.
$(use\pi =\frac{22}{7})$

1. $618.381c{m}^3$
2. $522.381c{m}^3$
3. $622.381c{m}^3$
4. $722.381c{m}^3$

Q. From the given diagram, find the ratio of the volume of the sphere to the volume of the cylinder.

Q.

Consider the following three statements.
Statement-1: Volume of a cylinder is equal to the $3$ times of the volume of a cone.

Statement-2: Total surface area of a cone $=$ curved surface area of the cone $+$ area of its base.

Statement-3 : Total surface area of a hemisphere of radius $r=2\pi r^2$.

Which of the following is correct?

1. Statements 1 and 3 are true and statement 2 is false.

2. Statements 2 and 3 are true and statement 1 is false.

3. Statements 1 and 2 are true and statement 3 is false.

4. Statements 2 and 3 are false and statement 1 is true.

Q.

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of the pillar to that of dome is 4:3, then what is the ratio of their volumes?

1. 2:1

2. 1:1

3. 3:1

4. 4:1

Q. For the two cones to have the same volume, their ______ should be the same.