Total surface area of a right circular cone

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.

Curved surface area of a cone is 308 $c{m}^2$ and its slant height is 14 cm.Find the radius of the base and total surface area of the cone.

Q. Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.

Q.

The volume of a right circular cone is 9856 $c{m}^3$.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 hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

Q.

The number of surfaces, a cone has, is

1. 1

2. 2

3. 3

4. 4

Q.

The slant height of a cone is increased by 10 %.If the radius remains the same, the curved surface area is increased by

1. 10%

2. 12.1%

3. 20%

4. 21%

Q. Q) The distance between the circular plates of a parallel plate condenser 40mm in diameter in order to have same capacity as a sphere of radius 1m is A) 0.01mm B) 0.1 mm C) 1.0mm D) 10mm

Q.

If the radius and slant height of a cone are in the ratio 7:13 and its curved surface area is 286 $c{m}^2$, find its radius.

Q.

A right circular cylinder just encloses a sphere of radius r (see figure). Find

(i) surface area of the sphere,

(ii) curved surface area of the cylinder,

(iii) ratio of the areas obtained in (i) and (ii).

Q. Hemispherical bowl is made of steel 0.25 cm thick. Inner radius of bowl is 5 cmfind outer CSA .

Q.

The radius of two similar right circular cones are $2cm$ and $6cm$. The ratio of their volumes is

1. $1:3$

2. $1:9$

3. $9:1$

4. $1:27$

Q. What is the total surface area of a cone of base radius r, height h and slant height l ?

1. $\pi rl$
2. $\pi r^2+\pi r^{2}l$
3. $\pi rl+\pi r^2$
4. $\pi r^2+2\pi rl$

Q.

If the circumference of the top of a hemispherical bowl is 22 cm. Its volume is

1. 80.73 cm³(app.)

2. 89.83 cm³(app.)

3. 76.33 cm³(app.)

4. 78.43 cm³(app.)

Q. The ratio of the radius and the height of a right cone is 5:9. Then the ratio of total surface area to curved surface of the cone is :

1. 2:3
2. 4:9
3. 18:13
4. 9:4

Q.

If the ratio of volume to total surface area of a solid sphere is 8 : 1, then radius of the sphere is ___.

1. $8$ units

2. $2\sqrt{2}$ units

3. $24$ units

4. $64$ units

Q.

The total surface area of a hemispherical bowl of diameter 28 cm is

1. 1600 cm²

2. 1800 cm²

3. 1648 cm²

4. 1848 cm²

Q.

The ratio of the radius to the height of a right cone is 3:4. Then the ratio of total surface area to curved surface of the cone is____.

1. 2:3

2. 3:5

3. 7:9

4. 8:5

Q.

A tent of height $33m$ is in the form of a right circular cylinder of diameter $120m$ and height $22m$ surmounted by a right circular cone of the same diameter Find the cost of canvas of the tent at the rate of $1.50Rsper{m}^2$.

Q. The ratio of the radius to the height of a right cone is 3:4. Then the ratio of total surface area to curved surface of the cone is

1. 2:3
2. 8:5
3. 5:8

Q. A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area of the shape if the length of the shape be 7 cm.

Q.

An ice cream cone has base radius 6 cm and altitude 8 cm. The total surface area of 21 such cones is

1. 5226 cm²

2. 4356 cm²

3. 5280 cm²

4. 6336 cm²

Q. Question 3 (i)
A cloth having an area of $165m^2$ is shaped into the form of a conical tent of radius 5 m.

(i) How many students can sit in the tent, if a student on an average occupies $\frac{5}{7}{m}^2$ on the ground?

Q. The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, the ratio of their curved surface areas, is

(a) 4 : 5

(b) 25 : 16

(c) 16 : 25

(d) 5 : 4

Q.

The curved surface area of a cone is $308c{m}^2$ and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.

Q. The ratio of the total surface area of a sphere and a hemisphere of same radius is

(a) 2 : 1

(b) 3 : 2

(c) 4 : 1

(d) 4 : 3

Q. Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm (Use $\mathrm{\pi }=3.14$)

Q. The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloons in two cases is
(a) 1 : 4
(b) 1 : 3
(c) 2 : 3
(d) 1 : 2

Q.

Find the volume of a cone with a radius of $6$ centimeters and a height of $15$centimeters. Round your answer to the nearest tenth.

Q. A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. [Use π = $\frac{22}{7}$]