Right Circular Cone and Its Surface Area

Q.

A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of Rs 25 per metre.

Q.

A military tent of height $8.25$ m is in the form of a right circular cylinder of base diameter $30m$ and height $5.5m$ surmounted by a right circular cone of same base radius. Find the length of canvas used in making the tent, if the breadth of the canvas is $1.5m.$

Q.

(i) A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre.

(ii) The radius and height of a solid right-circular cone are in the ratio of 5 : 12. If its volume is 314 $c{m}^3,$ find its total surface area. $[Take\pi =\mathrm{3.14.}]$

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 sector containing an angle of 120 degree is cut off from a circle of radius 21 cm and folded into a cone. Find the curved surface area of a cone.

1. $442c{m}^2$
2. $462c{m}^2$
3. $262c{m}^2$
4. $362c{m}^2$

Q.

The radius and height of a cone are in the ratio $4:3.$ The area of the base is $154c{m}^2$. The area of the curved surface in $c{m}^2$ is ___

Q.

The radius and height of right circular cone are in the ratio $4:3$ and its volume is $2156c{m}^3$. Find the curved surface area of the cone.

Q.

The height of a conical tent is 14 m and its floor area is 346.5 $m^2$. How much canvas, 1.1 m wide, will be required for it ?

(a) 490 m (b) 525 m (c) 665 m (d) 860 m

Q.

Why are conic sections called conic sections?

Q.

A cylindrical roller$2.5m$ in length, $1.75m$ in radius when rolled on a road was found to cover the area of $5500m^2$. How many revolutions did it make?

Q.

The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm, its volume is

1. 9000 cm³

2. 80080 cm³

3. 56090 cm³

4. 89009 cm³

Q. Total surface area of a cone of radius 5 cm and slant height 10 cm is .
$(Take\pi =3.14)$

1. $235.5c{m}^2$
2. $335.5c{m}^2$
3. $245c{m}^2$
4. $437c{m}^2$

Q.

The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is

(a) $60\pi c{m}^2$ (b) $65\pi c{m}^2$ (c) $30\pi c{m}^2$ (d) none of these

Q.

If the area of the base of a right circular cone is 3850 $c{m}^2$ and its height is 84 cm, find the slant height of the cone.

Q. Question 6
A shuttle cock used for playing badminton has the shape of the combination of
(A) a cylinder and a sphere
(B) a cylinder and a hemisphere
(C) a sphere and a cone
(D) frustum of a cone and a hemisphere

Q.

Three cubical blocks, each of volume 125 cm³, are joined end to end to form a cuboid. What is the total surface area of the cuboid so formed?

1. 350 cm²

2. 375 cm²

3. 425 cm²

4. 450 cm²

Q.

The volume of a sphere (in cubic cm) is equal to its surface area (in sq. cm). The diameter of the sphere (in cm) is

1. 6

2. 2

3. 3

4. 4

Q. The diameter of the base of a right circular cone is 42 cm and its height is 20 cm. Find the curved surface area of the cone.

1. $3300c{m}^2$
2. $1386c{m}^2$
3. $1914c{m}^2$
4. $26720c{m}^2$

Q.

The shape of a gulli in the gulli-danda game is a combination of

(a) a cone and a cylinder

(b) two cylinders

(c) two cones and a cylinder

(d) two cylinders and a cone

Q.

The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 $k{m}^2$. Find the height of the mountain.

Q.

Find the volume and surface area of a pyramid with height $3\sqrt{2}cm$ and a square base with sides all 6 cm in length [4 MARKS]

Q.

In a right circular cone, the cross section made by a plane parallel to the base is a

(a) sphere (b) hemisphere (c) circle (d) a semicircle

Q. The length of the diagonal of a cube that can be inscribed in a sphere of radius 7.5 cm is

Q.

A cone of radius 3 cm and slant height 5 cm has curved surface area of:

1. 13

2. 14

3. 15

4. 16

Q. Question 2
A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed.

Q. 5. A solid cylinder has diameter 28cm and height 24cm. A conical cavity of the same diameter and same height is drilled out from this solid. Find the whole surface area of the coni cal solid

Q. Question 5
The shape of a gilli, in the gilli-danda game ( see – figure) is a combination of

(A) two cylinders
(B) a cone and a cylinder
(C) two cones and a cylinder
(D) two cylinders and a cone

Q. The diameter of the base of a right circular cone is 42 cm and its height is 20 cm. Find the curved surface area of the cone.

1. $3300c{m}^2$
2. $1914c{m}^2$
3. $1386c{m}^2$
4. $26720c{m}^2$

Q. Question 3
A plumbline ( Sahul) is the combination of ( see figure)

(A) a cone and a cylinder
(B) a hemisphere and a cone
(C) frustum of a cone and a cylinder
(D) sphere and cylinder

Q.

The radius and height of a right circular cone are in the ratio 3:4. Then the ratio of total surface area of the cone to its curved surface area is

1. $2:3$

2. $3:5$

3. $7:9$

4. $8:5$