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

By actual drawing obtain the points equidistant from lines m and n; and 6 cm from a point P, where P is 2 cm above m, m is parallel to n and m is 6 cm above n. 

A straight line AB is 8 cm long. Draw and describe the locus of a point which is:

1. always 4 cm from the line AB.
2. equidistant from A and B.
   Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.

Draw a triangle ABC in which AB = 6 cm, BC = 4.5 cm and AC = 5 cm. Draw and label:

1. the locus of the centres of all circles which touch AB and AC,
2. the locus of the centres of all the circles of radius 2 cm which touch AB.
   Hence, construct the circle of radius 2 cm which touches AB and AC . 

The surface area of a sphere is 2464 cm², find its volume. 

The volume of a sphere is 38808 cm³; find its diameter and the surface area.

A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?

How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?

Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere. 

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.