T.S.A of the Cone

Q.

What is the formula of surface area and volume?

Q.

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

Q.

The total surface area of a cone whose radius is $\frac{r}{2}$and slant height $2l$ is:

A) $2\pi r(l+r)$
B) $\pi r(l+\frac{r}{4})$
C) $\pi r(l+r)$
D) ​​​​​​​$2\pi rl$​​​​​​​

Q. What will be the ratio of the total surface area of the cone to the total surface area of the sphere if, slant height of the cone is equal to the diameter of the base of the cone and radius of the cone is equal to radius of the sphere?

1. 3:4
2. 2:3
3. 3:2
4. 4:3

Q.

The ratio of base radius to slant height of a right circular cone is 3:2. Calculate the ratio of total surface area of cone to curved surface area of the cone.(Take $\pi =\frac{22}{7}$). [3 MARKS]

Q.

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

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

1. 5:4

2. 16:25

3. 4:5

4. 25:16

Q.

Question 9 (iii)
A right circular cylinder just encloses a sphere of radius r (see figure). Find:

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

Q. The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². Find the total suraface area of the cone.

1. $246.5c{m}^2$
2. $346.5c{m}^2$
3. $446.5c{m}^2$
4. $336.5c{m}^2$

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. 3:5

3. 7:9

4. 8:5

Q.

Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4:3.

Q.

Which of the following is false for a cone?

1. Volume of cylinder is twice that of volume of cone of same height and radius

2. Slant height is required to find the curved surface area of cone

3. Total surface area = $\pi$rl + $\pi$$r^2$

4. None of these

Q.

A solid sphere with centre 'O' of certain radius fits exactly into a right circular cone as shown in the diagram given below. If the volume of the sphere is 4186.67 ${cm}^3$, find the total surface area of the cone. (Take $\pi$ = 3.14). It is known that slant height of the cone is two times the radius of the base of the cone and the ratio of AO to DO is 2:1.

​

1. 400$\pi$ ${cm}^2$

2. 500$\pi$ ${cm}^2$

3. 900$\pi$ ${cm}^2$

4. 600$\pi$ ${cm}^2$

Q.

Dome of the enemy's fort is in shape of right cone which has slant height 13 m and height of 12 m as observed by the hero through the telescope.Hero comes to know that the dome is filled with gold. If the cost of gold is (30/π) lakhs per cubic meter. Find the total value of gold in the dome of the enemy's fort .(Take $\pi$= $\frac{22}{7}$)

1. 40 crores

2. 20 crores

3. 30 crores

4. 50 crores

Q. What will be the ratio of the total surface area of the cone to the total surface area of the sphere if, slant height of the cone is equal to the diameter of the base of the cone and radius of the cone is equal to radius of the sphere?

1. 3:4
2. 4:3
3. 3:2
4. 2:3

Q. Calculate the volume of a cone for the above figure : (Use $\pi =3$)

1. $27.7m^3$
2. $28.8m^3$
3. $26.8m^3$
4. $25.55m^3$

Q. A bus stop is barricaded from the remaining part of the road, by using $50$ hollow cones made of recycled cardboard. Each cone has a base diameter of $40cm$ and height $1m$. If the outer side of each of the cones is to be painted and the cost of painting is $₹12per{m}^2$, what will be the cost of painting all these cones? $(Use\pi =3.14$ and take $\sqrt{1.04}=1.02)$

Q. A bus stop is barricaded from the remaining part of the road, by using $50$ hollow cones made of recycled cardboard. Each cone has a base diameter of $40cm$ and height $1m$. If the outer side of each of the cones is to be painted and the cost of painting is $₹12per{m}^2$, what will be the cost of painting all these cones? $(Use\pi =3.14$ and take $\sqrt{1.04}=1.02)$

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. If mean of $n$ items is $\overline{x}$ , if each item is successively increased by $3,3^2,3^3...{.3}^n,$ then new means equals

1. $\overline{x}+\frac{3^{n+1}}{n}$
2. $\overline{x}+3\frac{(3^n-1)}{2n}$
3. $\overline{x}+\frac{3^n}{n}$
4. $\overline{x}+\frac{(3^n-1)}{2n}$

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. $2681c{m}^2$
2. $2861c{m}^2$
3. $2816c{m}^2$
4. $2618c{m}^2$

Q. A bus stop is barricaded from the remaining part of the road, by using $50$ hollow cones made of recycled cardboard. Each cone has a base diameter of $40cm$ and height $1m$. If the outer side of each of the cones is to be painted and the cost of painting is $₹12per{m}^2$, what will be the cost of painting all these cones? $(Use\pi =3.14$ and take $\sqrt{1.04}=1.02)$

Q.

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

1. $400{cm}^2$

2. $267{cm}^2$

3. $258{cm}^2$

4. $374{cm}^2$

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. $2681c{m}^2$