Surface Areas and Volumes MATHS - Surface Areas and Volumes

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 small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40m × 25m × 15m. For how many days will the water of this tank last?

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?

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.

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.