Frustum of a cone

Q.

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take $\pi =3.14$) [4 MARKS]

Q.

A drinking glass is in the shape of a frustum of a cone of height $14\mathrm{cm}$. The diameters of its two circular ends are $4\mathrm{cm}$ and $2\mathrm{cm}$. Find the capacity of the glass.

Q. Question 2 (ii)
Find the amount of water displaced by a solid spherical ball of diameter:
(ii) 0.21 m
$[Assume\pi =\frac{22}{7}]$

Q. Question 1
A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

Q.

Question 4
A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts

Q. Question 1
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.

Q. Question 3
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

Q.

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?

1. 262.39 m²

2. 662.39 m²

3. 563 m²

4. 463.39 m²

Q.

Question 1
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Q.

A chime is made of 3 identical spherical balls of density 363 g/$c{m}^3$. If mass of each ball is 49 g, then find radius of each ball.
Take $\pi =\frac{22}{7}$

1. $\frac{7}{22}$ cm

2. $\frac{22}{7}$ cm

3. $\frac{1}{21}$ cm

4. $\frac{2}{7}$ cm

Q. Lateral surface area of frustum of cone = $\pi (r_1+r_2)l$

1. True
2. False

Q.

What is the formula for the lateral surface area of the given frustum:

Where,
$R_1$ = radius of the base
$L$ = length of lateral side of the bigger cone of which the frustum is a part
$R_2$ = radius of the top surface
$l$ = length of lateral height of cone - lateral height of frustum(s) (L - s)

1. $\pi (R_{1}L-R_{2}l)$

2. $\pi R_1^{2}h-\pi R_{2}l$

3. $\pi (R_1^{2}h-R_2^{2}l)$

4. $\text{None of these}$

Q.

A bucket in form of a frustum of a cone which is to be painted is kept upside down. Find the area (in sq.cm) to be painted. Dimensions are in cm

1. 1474 cm²
2. 1956 cm²
3. 1936 cm²
4. 2090cm²

Q.

A well of whose diameter is 3m is dug 14m deep. The earth taken out of it is evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

1. 2.0 m

2. 3.87 m

3. 2.95 m

4. 1.125 m

Q.

Juice is filled upto 64 cm in a cylindrical container of radius 30 cm. It is served in small cylindrical cups of radius 6 cm and height 16 cm. If each cup is sold at Rs. 3, how much money can be earned by selling the juice?

1. Rs 100

2. Rs 900

3. Rs 600

4. Rs 300

Q.

I take a cone of Base radius $r_1$ and height $h_1$. I cut the cone on a plane parallel to its base. The cut is made at a height h from the base. After the cut I remove the cone. What is the name of the figure left out? What is the radius of its top surface?

1. r₁[1-(h/h₁)]

2. r₁[1-(h₁/h)]

3. r₁[(1-h)/h₁]

4. r₁

Q.

Question 12
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.

Q.

The diameter of a metallic sphere Is $6cm$. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire Is $36m$, Find the radius of its cross-section.

Q.

A chime is made of 3 identical spherical balls of density 363 g/$c{m}^3$. If mass of each ball is 49 g, then find radius of each ball.
Take $\pi =\frac{22}{7}$

1. $\frac{7}{22}$ cm

2. $\frac{22}{7}$ cm

3. $\frac{1}{21}$ cm

4. $\frac{2}{7}$ cm

Q. Question 5
Write ‘True’ or ‘False’ and justify your answer in the following
The volume of the frustum of a cone is $\frac{1}{3}\pi h[r_1^2+r_2^2-r_1{r}_2]$, where h is vertical height of the frustum and
$r_1,r_2$ are the radii of the ends.

Q. A milk carrying container has the shape of a cylinder mounted on a frustum. The radius of the cylinder is 14 cm and height is 20 cm. The other diameter of the frustum is 7 cm and its height is 5 cm. What is the curved surface area of the container?

1. $1880c{m}^2\left(approx\right)$
2. $2399.65c{m}^2\left(approx\right)$
3. $201.12c{m}^2\left(approx\right)$
4. $1060.5c{m}^2\left(approx\right)$

Q. Lateral surface area of frustum of cone = $\pi (r_1+r_2)l$

1. True
2. False

Q. If a hemisphere of radius 21 cm is melted and recast to form a cone of height 42 cm, then the radius of cone is ___.

1. 10 cm
2. 16 cm
3. 14 cm
4. 21 cm

Q. Lateral surface area of frustum of cone = $\pi (r_1+r_2)l$

1. True
2. False

Q.

Question 5
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Q. A cone hemisphere and a cylinder stands on equal bases and have the same height the height being equal to the radius of the circular base then their whole surface areas are in the ratio

1. $(\sqrt{3}+1):3:4$
2. $\sqrt{2}:3:4$
3. $\sqrt{3}:7:8$
4. $(\sqrt{2}+1):3:4$

Q.

The capacity of a closed cylindrical vessel of height 1 m is 15.4 l. How many square metres of the metal sheet would be needed to make it?

1. 4908 $c{m}^2$

2. 4708 $c{m}^2$

3. 5708 $c{m}^2$

4. 6718 $c{m}^2$

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.

Question 1
A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

Q. A milk carrying container has the shape of a cylinder mounted on a frustum. The radius of the cylinder is 14 cm and height is 20 cm. The other diameter of the frustum is 7 cm and its height is 5 cm. What is the curved surface area of the container?

1. $1880c{m}^2\left(approx\right)$
2. $2399.65c{m}^2\left(approx\right)$
3. $1060.5c{m}^2\left(approx\right)$
4. $201.12c{m}^2\left(approx\right)$