(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :

1. radii,
2. surface areas. 

If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.

The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:

1. radius
2. volume

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast. 

A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. 

Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm. 

A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.

The total area of a solid metallic sphere is 1256 cm². It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :

1. the radius of the solid sphere.
2. the number of cones recast. [Take π = 3.14]

A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.

A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl. 

Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm. 

Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?

A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere. 

A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid. 

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire. 

Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.

Calculate:

1. its volume,
2. the surface area of the tunnel (excluding the floor) and
3. its floor area.   

Find the value of k, if 2x + 1 is a factor of (3k + 2)x³ + (k − 1).