Frustum of a Cone

Q. Question 4
A container, opened from the top and 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 ₹ 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 8 per 100 square centimetres.

Q.

A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is $4.2cm$ and the heights of the cylindrical and conical portions are $12cm$ and $7cm$ respectively. The approximate volume of the toy will be

1. $250c{m}^3$

2. $200c{m}^3$

3. $218c{m}^3$

4. $300c{m}^3$

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 the frustum (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. $Noneofthese$

Q. A solid toy s in the form of a hemisphere surrounded by a right circular cone . The height of cone is 4 cm and the diameter of the base is 8 cm . Determine the volume of the toy. If a cube circumscribes the toy , then find the difference of the volumes of cube and the toy .

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

Q.

A bucket made of aluminium sheet is of height 20 cm and its upper and lower ends are of radius 25 cm and 10 cm respectively. Find the cost of making the bucket if the aluminium sheet costs Rs. 70 per 100 $c{m}^2$. (Use $\pi$ = 3.14).

Q. A container shaped like a right circular cylinder has a diameter (d) equal to 12 cm and height (h) equal to 15 cm is full of ice cream. The ice cream is to be filled into 10 equal cons having a hemispherical shape on the top. If the height of the cone is 4 times its radius, find the height of the cone.

Q.

The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is

(a) 41 (b) 43 (c) 49 (d) 51

Q.

A shuttle cock used for playing badminton has the shape of the combination of :

1. A cylinder and a hemisphere

2. A hemisphere and frustum cone

3. A cylinder and a sphere

4. A sphere and a cone

Q.

A solid consisting of a right circular cone standing on a hemisphere, is placed upright in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder having given that the radius of the cylinder is 3 cm and its height is 6 cm. The radius of hemisphere is 2 cm and the height of the cone is 4 cm. ( Also draw the diagram)

Q.

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

1. 1:6

2. 1:8

3. 1:4

4. 1:2

Q. A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is

(a) 15 cm

(b) 12 cm

(c) 10 cm

(d) 17 cm

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 hemispherical cup of radius 4 cm is filled to the brim with coffee. The coffee is then poured into a vertical cone of radius 8 cm and height 16 cm. What percentage of the cone remains empty?

1. 89.4%

2. 78.5%

3. 87.5%

4. 67.4%

Q. A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is

(a) 176 m³

(b) 196 m³

(c) 200 m³

(d) 110 m³

Q. A cylindrical container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. the whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.

Q.

The shape of a glass (tumbler) is usually in the form of

(a) a cylinder

(b) frustum of a cone

(c) a cone

(d) a sphere

Q.

A tent consists of a frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum are 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of the canvas required to make the tent. Assume that the radii of the upper end of the frustum and the base of the surmounted conical portion are equal. [2 MARKS]

Q. The parallel sides of a trapezium are 12 cm and 9 cm and the distance between them is 8 cm. Find the area of the trapezium.

Q.

A solid consists of a circular cylinder with an exact fitting circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is

1. 

2. 

3. 

4. 

Q. A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.

Q. The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is

(a) 6 cm

(b) 8 cm

(c) 4 cm

(d) 7 cm

Q. A cone of base radius 24 cm is cut by a plane parallel to its base exactly in the middle of its vertical height. If the vertical height of the cone is 14 cm, then volume of frustum is equal to

1. $8964.5c{m}^3$
2. $6908c{m}^3$
3. $2380c{m}^3$
4. $7392c{m}^3$

Q. Volume of a cylinder is three times the volume of a ___ having the same base and of the same height.

1. Another cylinder
2. Cube
3. Sphere
4. Cone

Q. A hemispherical lead of radius 8 cm is cast into a right circular cone of base radius 6 cm. Determine the height of the cone, correct to two places of decimal.

Q.

A hemisphere whose diameter is 4cm, made of wood . If the a cone cut out of this hemisphere whose base is also 4cm . Find the volume of wood in hemisphere .

Q. From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid. [CBSE 2011]

Q.

A shuttlecock used for playing badminton is the combination of

(a) cylinder and a hemisphere

(b) frustum of a cone and a hemisphere

(c) a cone and a hemisphere

(d) a cylinder and a sphere

Q. A friction clutch in the form of the frustum of a cone, the diameters of the ends being 8 cm, and 10 cm and length 8 cm. Find its bearing surface and its volume.\lbrack Take -3.14\rbrack

Q.

A toy is in the shape of a hemisphere of same base radius. If the volume of the toy is $231c{m}^2$ and it's diameter is $7cm$. find the height of the toy.