Curved Surface Area & Total Surface Area of Cone

Q. A cone of maximum size is carved out from a cube of edge 14 cm . Find the surface area of the cone and of the remaining solid left out after the cone carved out .

Q.

The formula for lateral surface area of cone is:

1. $\pi rh$
2. $\pi rl$
3. $\pi r^{2}h$
4. $\text{None of these}$

Q.

A cylinder is surmounted by a cone as shown in the figure. Find the total surface area solid formed. (in $c{m}^2$). (Take $\pi =3.14$)

1. 900

2. 855.05

3. 820.75

4. 830.75

Q.

A tent is in the form of a cylinder of diameter $4.2m$ and height $4m$, surmounted by a cone of equal base and height $2.8m$. find the cost of canvas for making the tent at ₹ $100$ per sq.m.

1. Rs $6590$

2. Rs $7590$

3. Rs $8590$

4. Rs $9876$

Q.

What is the base-radius and slant height of the cone made by rolling up a sector of radius 10 centimetres and central angle 60°?

Q.

What is the central angle of the sector needed to make a cone of base-radius 10 centimetres and slant height 25 centimetres?

Q.

The curved surface area of a cone is 440 sq. cm and slant height is 10 cm. Find the radius of the cone.

Q.

The height of a cone is 20 cm & the radius of its base is 15 cm. Find

1. 1177 cm², 1880 cm², 4000 cm³

2. 1170 cm², 1884 cm², 4530 cm³

3. 1170 cm², 1880 cm², 4920 cm³

4. 1177.50 cm², 1880 cm², 4000 cm³

5. 1177.50 cm², 1884 cm², 4710 cm³

6. 1177.50 cm², 1884 cm², 4000 cm³

Q.

What is the ratio of the base-radius and slant height of a cone made by rolling up a semicircle?

Q. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 105 cm and the diameter of the hemispherical ends is 36 cm each, find the cost of polishing the surface of the solid at the rate of 21 paise per square cm. [4 MARKS]

Q.

What is the curved surface area of a cone of base radius 12 centimetres and slant height 25 centimetres?

Q.

What is the curved surface area of a cone of base diameter 30 centimetres and height 40 centimetres?

Q.

Prove that for a cone made by bending a semicircle, the curved surface area is double the base area.

Q.

Anita is hosting a birthday party for her friends. She decided to make some conical party hats for her ten friends. The party hats are of height 24 cm with a radius of 7 cm made out of party paper. What is the total cost of the party paper if it costs $₹0.035perc{m}^2$?

1. 262.39 m²

2. 463.39 m²

3. 563 m²

4. 662.39 m²

Q. Along a path, 25 conical pillars are constructed. Each pillar has radius 15cm and height 20cm. Find the total cost of painting at the rate of Rupees 50 per centimeter square(take pie =3.14)

Q.

The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.

Q. Find slant height and radius of the cone made from quadrant of the circle of radius 9.6cm.

Q.

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7m and height of the cone is 1m, what is the area of cloth required? ($\sqrt{2}=1.414$)

1. 262.39 m²

2. 463.39 m²

3. 662.39 m²

4. 563 m²

Q.

There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. The ratio of their radii is

1. 2:1

2. 4:1

3. 2:5

4. 1:3

Q.

The ratio of base radius to slant height of a right circular cone is 4:3. Calculate the ratio of the total surface of the cone to the curved surface of the cone.(Take pi=$\frac{22}{7}$)

Q. Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Q.

A toy is in the form of a cone mounted on a hemisphere of radius $3.5cm.$ The total height of the toy is $15.5cm.$ Find the total surface area and volume of the toy $\left(use\pi =\frac{22}{7}\right)$.

Q.

If a sector of radius 9 cm with central 240⁰ is folded into a cone, the slant height of cone is

1. 6 cm

2. 2 cm

3. 3 cm

4. 9 cm

Q.

The diameter of the cone is 14 cm and slant height is 9 cm. Find the total surface area of the cone.

Q.

The central angle of 2 sectors of a circle is in the ratio of 4:5 and are used to make 2 cones. What is the ratio of their curved surface area?

1. 20

2. 16

3. 18

4. 12

Q. Question 7
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

Q. If the radius and the slant height of the cone are in the ratio of 4:7and its curved surface area is 792 cm^2 then its radius is

Q. A medicine capsule is in the shape of a cylinder with two hemisphere struck to each of its ends (see figure). The length of the entire capsule is $14mm$ and the diameter of the capsule is $5mm$. Find its surface area.

1. $240m{m}^2$
2. $280m{m}^2$
3. $220m{m}^2$
4. $120m{m}^2$

Q. The height of a right circular cone is trisected by two places drawn parallel to the base. Show that the volumes of the three portions starting from the top are in the ratio $1:7:19$.

Q. What is the pair of figures we would get if we cut open a right circular cone of radius $r$ and slant height $l$?

1. 
2. 
3. 
4. None of the above