C.S.A of the Cone

Q. The curved surface area of a cone is 2200 sq.cm and its slant height is 50 cm. Find the total surface area of cone.$\left(\mathrm{\pi }=\frac{22}{7}\right)$

Q.

The curved surface area of right circular cone whose slant height is 10 cm and base radius is 7 cm

Q.

The height of a right circular cone of radius 5 cm and slant height 13 cm is

1. 12 cm

2. 8 cm

3. 14 cm

4. 6 cm

Q.

The slant height of a cone with radius 15 cm and height 20 cm is

1. 21 cm

2. 20 cm

3. 15 cm

4. 25 cm

Q.

The curved surface area of a right circular cone whose slant height is 14 cm and base radius is 21 cm is

1. 232 cm²

2. 446 cm²

3. 308 cm²

4. 924 cm²

Q.

The curved surface area of a cone exceeds the base area by $88c{m}^2$. Its slant height exceeds the base radius by $4cm.$ Find the radius of the base.

Q. What's the curved surface area of the cone if the radius is 7 cm and the slant height is 14 cm?

1. 77 sq. cm
2. 154 sq. cm
3. 308 sq. cm
4. 254 sq. cm

Q. Curved surface area of a cone is 251.2 cm² and radius of its base is 8 cm. Find its slant height and perpendicular height. ($\mathrm{\pi }$ = 3.14 )

Q. Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height ( $\mathrm{\pi }$= 3.14)

Q. Find the total surface area of a cone of radius 2r and slant height l by 2

Q. Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.

Q. The radius and slant height of a cone are in the ratio 3:5. It's CSA is 2310cm². Find its radius.

Q.

the ratio of radii of two cones is 2 is to 3 and slant height is 9 is to 4 then ratio of their curved surface area is dash

Q. The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone.

Q. Assertion (A): Curved surface area of a right circular cone is
$\pi \times$ radius of base $\times$ slant height.

Reason (R): Total surface area of a right circular cylinder is
$\pi \times (radiusofbase{)}^2$ + $\pi \times$ radius of base $\times$ slant height.

Which of the following is correct?

1. Both A and R are true and R is the correct explanation of A.
2. Both A and R are true and R is not the correct explanation of A.
3. A is true and R is false.
4. A is false and R is true.

Q.

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone

Q.

A right circular cone has an altitude of $40cm$ and a diameter of $60cm.$ The slant height of the cone is

1. $25cm$

2. $50cm$

3. $30cm$

4. $20cm$

Q. The cost of painting a conical tent of radius $3.5m$ and slant height $7m$ at a rate of $₹10/m^2$ is .

1. $₹770$
2. $₹335$
3. $₹1,005$
4. $₹370$

Q.

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find

(i) radius of the base and (ii) total surface area of the cone.

Q. Question 8 (i)
A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find:
(i) the inside surface area of the dome,
$[Assume\pi =\frac{22}{7}]$

Q. The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is

(a) 2 : 1

(b) 4 : 1

(c) 8 : 1

(d) 1 : 1

Q.

The curved surface area of a right circular cone whose slant height is 28 cm and base radius is 10.5 cm is

1. 924 cm²

2. 1062 cm²

3. 748 cm²

4. 842 cm²

Q. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $122m,22m$ and $120m$ (see figure). The advertisements yield an earning of $Rs.5000per{m}^2$ per year. A company hired one of its walls for $3$ months. How much rent did it pay?

Q.

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

Q. The curved surface area of a cone is 4070 cm² and its diameter is 70 cm. What is its slant height? (Use = 22/7).

Q. Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.

Q. A cylinder and a cone have equal radii of these bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.

Q. The radius of a cone is 5 cm and vertical height is 12 cm. Find the area of the curved surface.

Q.

The diameters of two cones are equal. If their slant heights are in the ratio 3:4, then find the ratio of their curved surface areas.

1. 3 : 5

2. 5 : 4

3. 2 : 3

4. 3 : 4

Q. Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.