Question 1 :
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood .

Question 2 :
A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent.

Question 3 :
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

Question 4 :
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find its inner curved surface area.Assume $\pi$ =$\frac{22}{7}$.

Question 5 :
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the graphite .

Question 6 :
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Question 7 :
State true or false: If the radius of a cylinder is doubled and its curved surface area is not changed, then height must be halved.

Question 8 :
The total surface area of a cube is 96 $cm^2$. Find the volume of the cube.

Question 9 :
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.

Question 10 :
If the volume of a right circular cone of height 9 cm is 48 $\pi$ $cm^3$ , find the diameter of its base.

Question 11 :
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.What is the area of the glass?

Question 12 :
State true or false: A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

Question 14 :
State true or false: If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.

Question 15 :
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Question 16 :
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. Find the ratios of the surface areas of the balloon in the two cases.

Question 17 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23cf59b460d7261f56f.jpeg' /> In the above image, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.Assume $\pi$ =$\frac{22}{7}$.

Question 18 :
It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per $m^2$ , find radius of the base.

Question 19 :
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per $m^2$ is Rs 15000, find the height of the hall. [Hint : Area of the four walls = Lateral surface area.]

Question 20 :
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?