Relation between slant height and height of a right circular cone

Q.

The slant height of cone whose height and radius are $6cm$ and $8cm$ respectively is

1. $10cm$

2. $6cm$

3. $8cm$

4. $12cm$

Q.

If the volumes of two cones are in the ratio $1:4$ and their diameters are in the ratio $4:5,$ then the ratio of their heights, is

1. $1:5$

2. $5:4$

3. $5:16$

4. $25:64$

Q.

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

Q.

If the height and slant height of a cone are $21cm$ and $28cm$ respectively. Find its volume.

Q.

The Height Of A Cone Is$16cm$ And Its Base Radius Is $12cm$ $(\mathrm{\pi }=3.14)$. Find Its Slant Height.

Q.

From a solid cylinder whose height is $2.4$ cm and diameter $1.4$ cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $c{m}^2$.

Q.

The ratio of volumes of two cones is 4:5 and the ratio of the radii of their bases is 2:3.Find the ratio of their vertical heights.

Q.

If the heights of two cones are in the ratio 1:4 and the radii of their bases are in the ratio 4:1, then the ratio of their volumes is

1. 1:2

2. 2:3

3. 3:4

4. 4:1

Q.

The height of a cone is 21 cm.Find the area of the base if the slant height is 28 cm.

Q. For a cone of radius 'r', height 'h' and slant height 'l', $l^2=r^2+h^2$.

1. True
2. False

Q.

A right triangle with sides 3, 4 and 5 cms is first rotated about the side 4 cm to form a solid and then rotated about the side 3 cm to obtain another solid . The ratios of volumes of the 2 solids obtained is 1:1.

1. True

2. False

Q. Question 4
A conical tent is 10 m high and the radius of its base is 24 m. Find
(i) Slant height of the tent.
(ii) Cost of the canvas required to make the tent, if the cost of $1m^2$ canvas is Rs 70. $[Assume\pi =\frac{22}{7}]$

Q.

Question 3
In a right circular cone, height, radius and slant height need not always to be the sides of a right triangle.

Q. For a cone of radius 'r', height 'h' and slant height 'l', $l^2=r^2+h^2$.

1. True
2. False

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

1. 4:5
2. 25:16
3. 16:25
4. 5:4

Q. For a cone of radius 'r', height 'h' and slant height 'l', $l^2=r^2+h^2$.

1. True
2. False

Q. The slant height of a cone whose height and radius are 6 cm and 8 cm respectively is

1. 8 cm
2. 12 cm
3. 10 cm

Q. The base radii of two right circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes is

1. $r_2^2:r_1^2$
2. $9:25$
3. $25:9$

Q. If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ration of their heights is

1. 25 : 64
2. 5 : 4
3. 64 : 25
4. 5 : 16

Q. A cloth having an area of $165m^2$ is shaped into the form of a conical tent of radius $5m$.
Find the volume of the cone.

Q. The base radii of two right circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes is

1. $9:25$
2. $25:9$
3. $r_2^2:r_1^2$

Q. The slant height of a cone whose height and radius are 6 cm and 8 cm respectively is

1. 8 cm
2. 12 cm
3. 10 cm

Q.

Find the length of cloth used in making a conical pandal of height 100 m and base radius 240 m, if the cloth is 100$\pi$m wide.

Q.

The slant height of a cone whose height and radius are 6 cm and 8 cm respectively is _________.

1. 10 cm

2. 6 cm

3. 8 cm

4. 12 cm

Q. The slant height of a cone whose height and radius are 6 cm and 8 cm respectively is

1. 12 cm
2. 8 cm
3. 10 cm

Q.

The volume and the total surface area of a cone whose height and slant height are $12cm$ and $13cm$ respectively are ________.

1. 80π $c{m}^3$ and 90π $c{m}^2$
2. 100π $c{m}^3$ and 90π $c{m}^2$
3. 100π $c{m}^3$ and 80π $c{m}^2$
4. 85π $c{m}^3$ and 95π $c{m}^2$

Q. The slant height of a cone whose height and radius are 6 cm and 8 cm respectively is

1. 10 cm
2. 12 cm
3. 8 cm

Q. The base radii of two right circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes is

1. $9:25$
2. $r_2^2:r_1^2$
3. $25:9$
4. $2r_1^2:r_2^2$

Q. The base radii of two right circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes is

1. $2r_1^2:r_2^2$
2. $r_2^2:r_1^2$
3. $25:9$
4. $9:25$

Q. For a cone of radius 'r', height 'h' and slant height 'l', $l^2=r^2+h^2$.

1. True
2. False