Surface Area of Cone

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

1. 192.5 cm²
2. 152 cm²
3. 184.5 cm²
4. 162.5 cm²

Q.

A right angled triangle having its base and height equal to 24 $cm$ and 7 $cm$ respectively is rotated by 360⁰ along its base. Find the curved surface area of the resultant figure.

1. $520c{m}^2$
2. $550c{m}^2$
3. $450c{m}^2$
4. $1460c{m}^2$

Q.

The radius of a certain cone is 4 times the radius of a similar cone. The ratio of their altitudes is

1. 1: 16

2. 1 : 64

3. 1 : 4

4. 16 : 1

Q.

The ratio of areas of a circular field and a rectangular field is 1 : 2. Find the area of the rectangular field, if the area of the circular field is 50 m².

1. 25 m²

2. 50 m²

3. 100 m²

4. None of these

Q. Ratio of slant heights of two cones having equal diameters is 3 : 4. Ratio of their CSA is:

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

Q. CSA of cone of radius 'r', height 'h' and slant height 'l' is $\mathrm{\pi rl}$.

1. True
2. False

Q. The ratio of total surface area to curved surface of the cone is 8:5. Then the ratio of radius to height is____.

1. 7:6
2. 2:3
3. 3:4
4. 5:4

Q. A right triangle ABC with sides $5$cm, $12$cm and $13$cm is revolved about the side $12$cm. Find the volume of the solid so obtained.

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 triangle with sides $6$ cm, $8$ cm and $10$ cm is revolved about the side $8$ cm. Find the curved surface of the solid so formed.

1. $188.57$
2. $185.3$
3. $190.8$
4. $181.56$

Q.

A cone of radius 3 cm and slant height 5 cm has curved surface area of ___ $c{m}^2$.

1. 13$\pi$

2. 14$\pi$

3. 15$\pi$

4. 16$\pi$

Q.

A vessel is in the shape of a cube of side 30 $m$. How much water can it hold?

1. 29000 $m^3$
2. 27000 $m^3$
3. 26000 $m^3$
4. 28000 $m^3$

Q. CSA of cone of radius r, height h and slant height l is $\mathrm{\pi rl}$.

1. True
2. False

Q. If a cone has a radius of 5 cm and height of 12 cm, then match the following.

1. 13 cm
2. $90\pi c{m}^2$
3. $65\pi c{m}^2$

Q. If the radii of the ends of a bucket, 45 cm high, are 28 cm and 7 cm respectively, then the total surface area of the bucket is:

1. 8274 $c{m}^2$
2. 6074 $c{m}^2$
3. 7074 $c{m}^2$
4. 8074 $c{m}^2$

Q. CSA of cone of radius 'r', height 'h' and slant height 'l' is $\mathrm{\pi rl}$.

1. False
2. True

Q. A sphere ohas a radius of5cm measured to an accuracy of 0.1 cm. Find the percentage error in the measurement of its volume.

Q. A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio $8:5$, determine the ratio of the radius of the base to the height of either of them.

Q.

A circular ground of radius 50 $m$ has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is $625\pi m^2$, then the height of the tent is____$m$.

1. 96.8

2. 100.6

3. 88.5

4. 90.42

Q.

The diameters of two cones are equal. If their slant heights are in the ratio 3:4, then find the ratio of their curved surface areas.

1. 3 : 5

2. 3 : 4

3. 5 : 4

4. 2 : 3

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. $258{cm}^2$

3. $267{cm}^2$

4. $374{cm}^2$