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

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.

A sum of money is lent out at compound interest for two years at 20% p.a., being reckoned yearly. If the same sum of the money was lent Gut at compound interest of the same rate of percent per annum C.I., being reckoned half yearly would have fetched Rs. 482 more by way of interest. Calculate the sum of money lent out.

A sum of money amounts to ₹ 2,240 at 4 % p.a., simple interest in 3 years. Find the interest on the same sum for 6 months at 3`(1)/(2)`% p.a.

Use the factor theorem to determine that x - 1 is a factor of x⁶ - x⁵ + x⁴ - x³ + x² - x + 1.

Use the factor theorem to factorise completely x³ + x² - 4x - 4.

Find the value of a , if (x - a) is a factor of x³ - a²x + x + 2.

If (x - 2) is a factor of the expression 2x³ + ax² + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.

Show that (x - 1) is a factor of x³ - 7x² + 14x - 8. Hence, completely factorise the above expression.

Given that x + 2 and x + 3 are factors of 2x³ + ax² + 7x - b. Determine the values of a and b.

In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x³ - 3x² + 4x - 4 and g(x) = x - 2