Total Surface Area of a Right Circular Cone

Q. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area. [4 MARKS]

Q.

The total surface area of a right circular cone of slant height 13 cm is 90$\pi$ $c{m}^2$. Calculate :
(i) its radius in cm,
(ii) its volume in $c{m}^3$, in terms of $\pi$.

Q. Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m and the canvas to be used costs Rs 100 per sq m. Find amount the associations will have to pay. What values are shown by these associations?

Q. Question 3
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Q.

The surface area of a cylinder which exactly fits in a cube of side $b$ is __________.

Q.

The radius and height of a right cone are in the ratio $3:4.$ 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.

The base of a conical tent is of area $616$ sq. cm. A $48$ cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

1. $2816c{m}^2$

2. $2861c{m}^2$

3. $2618c{m}^2$

4. $2681c{m}^2$

Q.

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are $10$ cm and $7$ cm respectively. The area of aluminium sheet required to make the cone is
(Use $\pi =3.14$)

1. 

2. 

3. 

4. 

Q.

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

1. 2:3

2. 3:5

3. 7:9

4. 8:5

Q.

A conical shaped container with a height of 30 cm has the area of its base equal to 100 $c{m}^2$. Find the number of grapes (spherical in shape) that can be put in the container if each grape has a radius of 0.42 cm.

1. 312

2. 322

3. 332

4. 302

Q. For a cylinder of radius 'r' and height 'h', TSA = and CSA = .

1. 2πrh

2. 2πrh + πr${}^2$

3. 2πr(r+h)
4. πr${}^2$

Q.

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cubic units and the total surface area is 312 square units. The length of the longest edge is

1. 12

2. 16

3. 18

4. 20

Q.

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

1. Rs 6590

2. Rs 7590

3. Rs 8590

4. Rs 9876

Q.

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

1. 3:5

2. 2:3

3. 7:9

4. 8:5

Q. Twenty-seven solid iron spheres, each of radius r and surface area s are melted to form a sphere with surface area s'. The radius (r) of the new sphere k is

1. 5
2. 4
3. 3
4. $\frac{5}{3}$

Q. TSA of cone of radius 'r', height 'h' and slant height 'l' is πr${}^2$h+πr${}^2$

1. True
2. False

Q. A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio $5:12$ respectively, then the ratio of the total surface area of the cylinder to that of the cone is __________.

1. $17:9$
2. $3:1$
3. $13:9$
4. $34:9$

Q.

A closed hollow cone 24 cm high having base radius 7 cm is to be made using metal sheets. Find the capacity of the cone and the amount of sheet required to make the cone.

1. $704c{m}^2$ and $1232c{m}^3$ respectively

2. $514c{m}^2$ and $1032c{m}^3$ respectively

3. $1232c{m}^2$ and $704c{m}^3$ respectively

4. $804c{m}^2$ and $1532c{m}^3$ respectively

Q. A metal sheet of breadth 10 cm is used to make a cone of radius 14 cm and slant height 20 cm. Then length of sheet if 25% of sheet is wasted is .

1. $1.99m$
2. $1.77m$
3. $1.82m$
4. $1.54m$

Q.

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is(Use $\pi =3.14$)

Q. A conical shaped container with a height of 30 cm has the area of its base equal to 100 $c{m}^2$. Find the number of grapes (spherical in shape) that can be put in the container if each grape has a radius of 0.42 cm.

Q.

Question 6
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Q. An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is $85$ m and height of the cylindrical part is $50$m. If the diameter of the base is $168$m, find the quantity of canvas required to make the tent. Allow $20$ extra for fold and far stitching. Give your answer to the nearest $m^2$.

1. $504053.012$
2. $50553.702$
3. $40423.712$
4. $50423.712$

Q. The base of a conical tent is of area 616 sq. cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?
$\left[3Marks\right]$

Q.

The base of a conical tent is of area 616 sq. cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

Q.

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. The area of aluminium sheet required to make the cone is(Use $\pi =3.14$

Q.

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. Find the area of aluminium sheet required to make the cone.(Use $\pi =\frac{22}{7}$)

1. 

2. 

3. 

4. 

Q. Due to sudden floods, some welfare associations jointly requested the government to get $100$ tents fixed immediately and offered to contribute $50\%$ of the cost. If the lower part of each tent is of the form of a cylinder of diameter $4.2$ m and height $4$ m with the conical upper part of the same diameter but height $2.8$ m, and the canvas to be used costs Rs. $100$ per sq. m, find the amount, the associations will have to pay. What values are shown by these associations $[Use\pi =\frac{22}{7}]$

Q. The base of a conical tent is of area 616 sq. cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?