Surface Areas a...

Let 'a' and 'b' respectively be the radius of the base and the height of a right circular cylinder. Which of the following expressions represents the ratio of its curved surface area to its total surface area?

A cylinder of height 7 cm and diameter 44 cm is melted to form cubes, each of side 2 cm. Calculate the number of cubes formed.

If the total surface area of a right circular cone with base radius 6 cm is 96 cm², then its altitude is

A sphere is melted and recast into smaller right cones of height 7 centimeters and radius 7 centimeters. If the radius of the sphere is 7 meters, then how many cones can be made?

Two right circular cones have equal slant height. If the ratio of their base radii is 5 : 3, then the ratio of their curved surface areas is

A hemisphere, a cylinder and a cone are joined as shown in the figure.



If C₁, C₂ and C₃ respectively are the curved surface areas of the hemisphere, the cylinder and the cone, then which of the following expressions represents the total surface area of the figure?

A circus tent is in the form of a cone over a cylinder. The diameter of the base is 6 m, the height of the cylindrical part is 15 m and the total height of the tent is 19 m. The canvas required for the tent is

A metallic right circular cone of height 9 cm and base radius 7 cm is melted to form a cuboid with two sides measuring 11 cm and 6 cm. The third side of the cuboid measures

If a square is rotated along one of its diagonals, then find the curved surface area of the shape formed by it, given that one of its side is 9 metres.

The height of a frustum made from a cone is 8 cm. If the base radii of this frustum are 6 cm and 2 cm, then find the height of the original cone.

A spherical ball of radius 7 cm is melted and recast into 8 small balls of the same radius. The radius of each smaller ball is

The height of a cone is 40 cm. A small cone is cut off from the top by a plane parallel to its base. If the volume of the frustum left out is of the volume of the original cone, find the height of the cone cut off from it.

The sector of a circle with radius 10 cm and angle 120° is rolled up such that the two bounding radii are joined together to form a cone. Find the volume of the cone.

The length, breadth and height of a cuboid are 10 m, 6 m and 5 m, respectively. It is melted and converted into 10 equal cubes. In this process, 10% of the material is lost. What is the length of the edge of each cube?

Let be the slant height of a frustum. If a and b represent the two base radii, which of the following expressions represents the ratio of the total surface area to the curved surface area of the frustum?

A toy is made in the form of a hemisphere surmounted by a right circular cone whose circular base coincides with the plane surface of the hemisphere. The base radius of the cone is 3.5 m and its volume is (2/3)^rd of the volume of the hemisphere. Calculate its height.

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m, while the vertex of the cone is 16 m above the ground. What is the area of the curved surface for the conical portion?

Ram cuts a semicircle of radius 8 cm from a piece of paper and folds it in such a way that it forms a right circular cone. What is the volume of this cone?

An oil tanker is in the form of a right circular cylinder of outer radius 10 cm and depth 25 cm. The thickness of the tanker's outer layer is 2 cm. Find the cost of the oil filling in the tanker, if it costs 5 paisa per cubic cm.

If one cubic cm of cast iron weighs 21 g, then find the weight of a pipe made of cast iron having length 1 m, internal diameter 3 cm and thickness 1 cm.

A solid metal sphere is melted and smaller spheres, all with the same radius, are formed. 20% of the material is lost in this process. The radius of each smaller sphere is the radius of the original sphere. If 20 litres of paint was needed to paint the original sphere, then how many litres of paint would be required to paint all the smaller spheres?

Water in a canal, 30 dm wide and 12 dm deep, is flowing with a velocity of 100 km per hour. How much area will it irrigate in 30 minutes, if 8 cm of standing water is required?

A sphere of radius 3 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cross-section of the vessel is 12 cm. After the sphere is completely submerged in water, the rise in the water level in the vessel is

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 5 m and 8 m, respectively, and the slant height of the top is 1.4 m, find the cost of the canvas of the tent at the rate of Rs. 200 per m². It is to be noted that the tent has no base.

The height of a right circular cone and the radius of its circular base are 9 cm and 3 cm, respectively. The cone is cut by a plane parallel to its base so as to divide it into two parts. The volume of the frustum (i.e. the lower part) of the cone is 44 cubic cm. The radius of the upper circular surface of the frustum (taking = ) is