Total surface area of a right circular cone

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

Q.

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

1. $2:3$

2. $8:5$

3. $7:9$

4. $3:5$

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. A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is $26cm$, while the height of the conical part is $6cm$. The base of the conical portion has a diameter of $5cm$, while the base diameter of the cylindrical portion is $3cm$. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours (Take $\pi =3.14$)

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

Q.

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

1. 3020

2. 312

3. 322

4. 3225