Volume of a Frustum

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 16 cm and 12 cm. Find the capacity of the glass.

Q. The radius and the slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 $c{m}^2$, find its radius $(use\pi =\frac{22}{7})$ [3 MARKS]

Q.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

Q.

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 $c{m}^3$ of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use $\pi$ = 3.14)

Q. Question 7
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per $m^2$. (Note that the base of the tent will not be covered with canvas.)

Q. A cone of radius 4 cm is divided into two parts by drawing a plane through the mid point of its axis and parallel to its base . Compare the volumes of two parts.

Q.

The radii of the circular bases of a frustum of a right cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

Q. Question 1 (ii)
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:
(ii)The cost of the sheet for it, if a sheet measuring $1m^2$ costs Rs. 20.

Q.

A container made of a metal sheet open at the top is of the form of frustum of cone, whose height is 16 cm and the radii of its lower and upper circular edges are 8 cm and 20 cm respectively. Find

(i) the cost of metal sheet used to make the container if it costs Rs 10 per 100 $c{m}^2$

(ii) the cost of milk at the rate of Rs 35 per litre which can fill it completely.

Q.

A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use $\pi =3.14$). [3 MARKS]

Q.

A solid is in the shape of a frustum of a cone. The diameters of the two circular ends are 60 cm and 36 cm and the leight is 9 cm. Find the area of its whole surface and the volume.

Q.

The perimeters of the two circular ends of a frustum of a cone are 48 cm and 36 cm. If the height of the frustum is 11 cm, find its volume and curved surface area.

Q.

Q. A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 21 per litre.
(Use $\mathrm{\pi }=\frac{22}{7}$)

Q.

If the radii of circular ends of frustum of a cone are 20 cm and 12 cm and its height is 6 cm, then the slant height of frustum (in cm) is:

1. 10

2. 15

3. 8

4. 12

Q.

Q.

Q.

Find the volume of a cone. Round your answer to the nearest tenth.

Q.

A bucket has top and bottom diameters of 40 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin used for making the bucket at the rater of Rs.1.20 per $d{m}^2$ (Use $\pi$= 3.14)

Q.

The height of a cone is 10 cm. The cone is divided into two parts usign a plane parallel to its base at the middle of its height. Find the ration of the volumes of two parts.

Q. The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.($\mathrm{\pi }=\frac{22}{7}$)

circumference₁ = 2$\mathrm{\pi }$r₁ = 132

r₁ = $\frac{132}{\mathrm{\pi }}=\boxed{134}$

circumference₂ =2$\mathrm{\pi }$r₂= 88

r₂= $\frac{88}{2\mathrm{\pi }}=\boxed{134}$

slant height of frustum, l = $$\begin{gathered} \sqrt{h^2+{\left(r_1-r_2\right)}^2} \\ \sqrt{{\boxed{1223}}^2+\boxed{1234}{}^2} \\ =\boxed{1234}\mathrm{cm} \end{gathered}$$

curved surface area of the frustum = $\mathrm{\pi }$ (r₁ + r₂ ) l

= $$\begin{gathered} \mathrm{\pi }\times \boxed{123}\times \boxed{132} \\ =\boxed{123}\mathrm{sq}.\mathrm{cm}. \end{gathered}$$

Q. If the slant height of the frustum of a cone is 6 cm and the perimeters of its circular bases are 24 cm and 12 cm respectively. What is the curved surface area of the frustum?

Q.

A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and surface area of the bucket. Also, find the cost of milk which can completely fill the cointainer, at the rate of Rs.25 per litre. (Use $\pi$ = 3.14)

Q. An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket. Also, find the volume of water the bucket can hold, in litres.

Q.

Slant height of the pyramid will be greater than the Height of the pyramid.

1. False

2. True

Q. A tent is in the form of a cylinder of diameter 15 m and height 2.4 m, surmounted by a cone of equal base and height 4 m. Find the capacity of the tent and the cost of the canvas at Rs. 50 per square meter.

Q.

A container in the shape of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely filled with oil. If each $c{m}^3$ of oil has mass 1.2 g then find the cost of oil in the container if it costs Rs 40 per kg.

Q.

A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of Rs 30 per litre, which the bucket can hold.

Q. Question 5
A metallic right circular cone 20 cm high and whose vertical angle is ${60}^{\circ }$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, find the length of the wire.

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