Surface Areas and Volumes Maths - Surface Areas and Volumes

Write True or False and justify your answer in the following:
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.

Write True or False and justify your answer in the following:
The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

Write True or False and justify your answer in the following:
If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.

Write True or False and justify your answer in the following:
In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Write True or False and justify your answer in the following:
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

How many square metres of canvas is required for a conical tent whose height is 3.5m and the radius of the base is 12m?

A shopkeeper has one spherical laddoo of radius 5cm. With the same amount of material, how many laddoos of radius 2.5cm can be made?

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

A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625m³. If the present depth of water is 1.3m, find the volume of water already used from the tank.

A school provides milk to the students daily in a cylindrical glasses of diameter 7cm. If the glass is filled with milk upto an height of 12cm, find how many litres of milk is needed to serve 1600 students.

A cylindrical roller 2.5m in length, 1.75m in radius when rolled on a road was found to cover the area of 5500m². How many revolutions did it make?

A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. Find the capacity of the cup.

Two solid spheres made of the same metal have weights 5920g and 740g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5cm.

The water for a factory is stored in a hemispherical tank whose internal diameter is 14m. The tank contains 50kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

A cylindrical tube opened at both the ends is made of iron sheet which is 2cm thick. If the outer diameter is 16cm and its length is 100cm, find how many cubic centimeters of iron has been used in making the tube?

30 circular plates, each of radius 14cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find:

1. The total surface area.
2. Volume of the cylinder so formed.

The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.

A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?