Volume of Frustum of a Cone

Q.

A clown’s cap is in the shape of a cone of height 8cm and diameter 12cm. A cut is made from the apex of the cone such that slant height of the newly formed cone is 5cm. Find the ratio of volume of the frustum of the cone formed due to the cut to the volume of the cap.

1. 0.3

2. 0.325

3. 0.35

4. 0.875

Q.

The radius of the base of a right circular cone is r. It is cut by a plane parallel to the base at a height h from the base.

The slant height of the frustum is $\sqrt{h^2+\frac{4}{9}{r}^2}$ . Show that the volume of the frustum is $\frac{13}{27}\pi r^{2}h$

Q. The slant height of a frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. What is the curved surface area of the frustum?

1. $48c{m}^2$
2. $96c{m}^2$
3. None of these
4. $24c{m}^2$

Q. Question 2
The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

Q.

A frustum of height 14 cm and radii 3 cm and 9 cm is filled with water upto the brim. Find the quantity of water in the frustum.

1. $572c{m}^3$
2. $1716c{m}^3$
3. $5148c{m}^3$
4. $1700c{m}^3$

Q. A container made up of a metal sheet is in the form of a frustum of a cone of height $14cm$ with radii of its lower and upper ends as $4cm$ and $10cm$ respectively. Find the approximate cost of the milk which can completely fill the container at the rate of ₹30 per liter.

1. ₹57
2. ₹60
3. ₹68
4. ₹69

Q.

The radius of the base of a right circular cone is r. It is cut by a plane parallel to the base at a height h from the base. What is the volume of the frustum obtained if it's slant height is $\sqrt{h^2+\frac{4}{9}{r}^2}$.

1. $\frac{27}{13}\pi r^{2}h$

2. $\frac{1}{3}\pi r^{2}h$
3. $\frac{13}{27}\pi r^{2}h$
4. $\frac{13}{26}\pi r^{2}h$

Q. The radius and height of a right circular cone are in the ratio $1:2$. If its volume is $144\pi {cm}^3$, then its slant height = .

1. 5 $\sqrt{5}$ cm
2. 4 $\sqrt{5}$ cm
3. 6 $\sqrt{5}$ cm
4. 5 $\sqrt{6}$ cm

Q.

A container, open from the top and made of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost (in rupees) of the milk which can completely fill the container, at the rate of ₹ 20 per litre.

Also, find the cost (in rupees) of metal sheet used to make the container, if it costs ₹ 8 per 100$c{m}^2$. (Take $\pi$ = 3.14).

1. 221; 156.75

2. 209; 156.75

3. 209; 162.5

4. 221; 162.5

Q. If the radii of the ends of a bucket, 45 cm high, are 28 cm and 7 cm respectively, then the total surface area of the bucket is:

1. 6074 $c{m}^2$
2. 7074 $c{m}^2$
3. 8074 $c{m}^2$
4. 8274 $c{m}^2$

Q. The slant height of a frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. What is the curved surface area of the frustum?

1. None of these
2. $24c{m}^2$
3. $48c{m}^2$
4. $96c{m}^2$

Q.

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass(in $c{m}^3$).

1. $\frac{308}{3}$

2. $\frac{316}{3}$

3. $\frac{301}{3}$

4. $\frac{320}{3}$

Q.

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each $c{m}^3$ of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take $\pi$ = $\frac{22}{7}$)

1. 10

2. 12

3. 14

4. 16

Q.

The radius of the base of a right circular cone is r. It is cut by a plane parallel to the base at a height h from the base. What is the volume of the frustum obtained if it's slant height is $\sqrt{h^2+\frac{4}{9}{r}^2}$.

1. $\frac{27}{13}\pi r^{2}h$

2. $\frac{1}{3}\pi r^{2}h$
3. $\frac{13}{27}\pi r^{2}h$
4. $\frac{13}{26}\pi r^{2}h$

Q. Volume of the given frustum of a cone
$=\frac{1}{3}\pi h({r_1}^2+r_1{r}_2+{r_2}^2)$

1. False
2. True

Q. Arrange the solids in ascending order (from top to bottom) of volumes, where $l=b=h=r$.

1. Cuboid
2. Cone
3. Cylinder
4. Sphere