Volume of Cone

Q.

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. find the volume and the curved surface area of the solid so formed.

Q. If the radius and the height of a cone is 3 cm and 4 cm respectively, then its slant height is .

1. 5 cm
2. 4 cm
3. 7 cm

Q.

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of the volumes of the upper part of the cone and the entire cone is:

1. $1:2$

2. $1:4$

3. $1:6$

4. $1:8$

Q. Question 9
A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.
The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required.
$[Assume\pi =\frac{22}{7}]$

Q. The slant height (l) of a cone of radius r and height h is

1. $\sqrt{r^2+h}$
2. $r^2+h^2$
3. $\sqrt{r^2+h^2}$
4. $(r^2+h^2{)}^2$

Q.

A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how many litres of water can the bucket hold? (Take $\pi$ = $\frac{22}{7}$)

1. 28.49 litres

2. 27.49 litres

3. 26.49 litres

4. 25.49 litres

Q.

Two cones have the same volume and their base radii are in the ratio $3:4$. What is the ratio of their heights?

1. $9:25$

2. $25:16$

3. $16:25$

4. $16:9$

Q. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. The heap is to be covered by canvas to protect it from the rain. Find the volume of the heap and the area of the canvas required.

1. $86.625m^3$, $99.825m^2$
2. $99.625m^3$, $86.825m^2$
3. $26.625m^3$, $86.825m^2$
4. $99.625m^3$, $56.825m^2$

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.

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. The capacity of the glass is $102\frac{2}{3}c{m}^3$.

1. True

2. False

Q.

Paul wants to put 1200 steel ball bearings (which are spherical in shape) with a radius of 5 mm, into a cylindrical container which is 30 cm high and 18 cm in diameter. Will all the bearings fit into the container?

Q.

The radii of the circular ends of a conical curd container, $6cm$ high are $16cm$ and $24cm$. Find the volume of the container in litres.(take $\mathrm{\pi }=3.14)$

Q. The volume of a conical pencil is $4928{in}^3$. If the radius of the base is $4$ in. Find its slant height of the conical pencil. Its original height is $10$ in.

1. $11.77in$
2. $14.77in$
3. $10.77in$
4. $12.77in$

Q.

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameter of its two circular ends are 4 cm and 2 cm. The capacity of the glass is $102\frac{2}{3}c{m}^3$.

1. 

2. 

Q.

Find the volume of water which can be filled in a bucket of height 8 cm and radii of ends of the bucket are 9 cm and 3 cm.

1. $312\pi c{m}^3$

2. $108\pi c{m}^3$

3. $324\pi c{m}^3$

4. $321\pi c{m}^3$

Q. Match the following objects to their volume.

1. $\pi$$r^{2}h$
2. $\frac{1}{3}\pi r^{2}h$
3. $lbh$
4. $l^3$

Q. A clay ball was split in half and its insides is scooped out. If the hollow shape formed is a hemisphere of inner radius $3cm$ and has a thickness of $3cm$. Find the total volume of the clay remaining in both the halves.

1. $679c{m}^3$
2. $712c{m}^3$
3. $759c{m}^3$
4. $792c{m}^3$

Q.

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

1. 210

2. 110

3. 200

4. 100

Q.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

1. 0.375

2. 0.625

3. 0.125

4. 0.875

Q.

The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to the base. If the volume of the small cone be $\frac{1}{64}$ of the volume of the given cone, at what height ( in cm) above the base is the section made ?

1. 20

2. 30

3. 40

4. 50

Q.

The volume of the cone is

1. Square of its radius multiplied by 2π

2. Third of the product of the base area and height.

3. The square of its radius multiplied by 4π.

4. Half of the product of the base area and height.

Q.

A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how many litres of water can the bucket hold? (Take $\pi$ = $\frac{22}{7}$)

1. 28.49 litres

2. 27.49 litres

3. 26.49 litres

4. 25.49 litres

Q.

A container made up 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 of the milk which can completely fill the container at the rate of ₹ 15 per litre. (Take $\pi$= 3·14)

1. 97.97

2. 100

3. 92.45

4. 95.63

Q.

Paul wants to put 1200 steel ball bearings (which are spherical in shape) with a radius of 5 mm, into a cylindrical container which is 30 cm high and 18 cm in diameter. Will all the bearings fit into the container?

Q. Two similar cones have volumes $12\pi$ cu. units and $96\pi$ cu. units. If the curved surface area of the smaller cone is $15\pi$ sq. units, what is the curved surface area of the larger one?

Q. Match the following :
$\begin{array}{cc}\text{A. Volume of Cone}& i.\pi r^{2}h\\ \text{B. Volume of Sphere}& ii.\frac{4}{3}\pi r^3\\ \text{C. Volume of Cylinder}& iii.\frac{\left(\pi r^{2}h\right)}{3}\end{array}$

1. A - iii, B - ii, C - i
2. A - ii, B - i, C - iii
3. A - i, B - iii, C - ii
4. A - iii, B - i, C - ii

Q. If h, s, V the height, curved surface area and volume of a cone respectively, then
$\left(3\pi V{h}^3+9V^2-s^2{h}^2\right)=?$

Q. Match the following :
$\begin{array}{cc}\text{A. Volume of Cone}& i.\pi r^{2}h\\ \text{B. Volume of Sphere}& ii.\frac{4}{3}\pi r^3\\ \text{C. Volume of Cylinder}& iii.\frac{\left(\pi r^{2}h\right)}{3}\end{array}$

1. A - iii, B - ii, C - i
2. A - ii, B - i, C - iii
3. A - i, B - iii, C - ii
4. A - iii, B - i, C - ii

Q. Fill in the blanks to make the statement true.
The volume of a cylinder which exactly first in a cube of side a is ________.

Q.

A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how many litres of water can the bucket hold ? (Take $\pi$ = $\frac{22}{7}$)

__