C.S.A of the Cone

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. 5 : 4

3. 2 : 3

4. 3 : 4

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

Q.

The height and radius of cone are $4cm$ and $3cm$ respectively. Find the curved surface area of cone.

1. $14\pi {cm}^2$

2. $15\pi {cm}^2$

3. $16\pi {cm}^2$

4. $12\pi {cm}^2$

Q.

In a birthday, 25 caps are required which are of conical shape. The dimensions of conical cap must be 10 cm (height) and 24 cm (radius). If the material used for making these caps is paper which is in rectangular shape. The length of paper is 24 cm, then the width of paper is ________.

1. 24π cm

2. 52π cm

3. 26π cm

4. 72π cm

Q.

If the area of a rectangle is equal to the curved surface area of the cone, then find the breadth of the rectangle in terms of radius$\left(r\right)$, slant height$\left(h\right)$ and length $\left(l\right)$.

1. $\frac{\pi lh}{r}$
2. $\frac{\pi rh}{l}$
3. $\frac{\pi rl}{h}$

4. $\frac{hrl}{\pi }$

Q. The slant height of a cone is increased by $10\%$. If the radius remains the same, the curved surface area is increased by _____.

1. $10\%$
2. $12.1\%$
3. $20\%$
4. $21\%$

Q. Assertion (A): Curved surface area of a right circular cone is
$\pi \times$ radius of base $\times$ slant height.

Reason (R): Total surface area of a right circular cylinder is
$\pi \times (radiusofbase{)}^2$ + $\pi \times$ radius of base $\times$ slant height.

Which of the following is correct?

1. Both A and R are true and R is the correct explanation of A.
2. Both A and R are true and R is not the correct explanation of A.
3. A is true and R is false.
4. A is false and R is true.

Q. If the curved surface area of $con{e}_1$ is twice the curved surface area of $con{e}_2$, then what's the relation between their radii and slant heights ?

1. $2r_1{l}_1=r_2{l}_2$
   
2. $r_1{l}_1=2r_2{l}_2$
   
3. $2r_2{l}_1=r_1{l}_2$
   
4. $\frac{2r_1}{l_1}=\frac{r_2}{2l_2}$
   

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 cost of painting a conical tent of radius $3.5m$ and slant height $7m$ at a rate of $₹10/m^2$ is .

1. $₹770$
2. $₹335$
3. $₹1,005$
4. $₹370$