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

How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?

A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere . 

A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder . 

Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm . 

The sum of first 14 terms of an A.P. is 1050 and its 14^th term is 140. Find the 20^th term.

Find the sum of first 10 terms of the A.P.

4 + 6 + 8 + .............

Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.

How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?

The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.

A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm.  How many containers are necessary to empty the bowl?

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: the number of cones recasted [π = 3.14]

The surface area of a solid metallic sphere is 2464 cm². It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate : the number of cones recast.  `("Take"  pi =22/7)`

From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the volume of remaining solid 

From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the weight of the material drilled out if it weighs 7 gm per cm³.

The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.

Calculate :

1. the total surface area.
2. the total volume of the solid and
3. the density of the material if its total weight is 1.7 kg.

A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.

A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area. 

Find the Compound Interest on Rs. 2,000 for 3 years at 15% per annum Compounded annually.

Find the difference between the simple interest and compound interest on 2,500 for 2 years at 4% p.a., compound interest being reckoned semi-annualy.