Surface Areas a...

A sphere of copper, whose diameter is 18 cm, is melted and converted into a wire of 4 mm diameter. Length of the wire (in meters) is

A right circular cone is cut into two pieces by a plane parallel to its base. The base radii of the frustum thus formed are 'a' and 'b' (a > b). If 'h' is the height of the frustum, then find the height of the smaller cone.

If both the radii of a frustum are doubled, keeping the height unchanged, then how many times will the new volume of the frustum be as compared to the original volume?

A cone with radius 7 m has volume 1232 m³. What is the cost of painting the curved surface of the cone at the rate of Rs. 20 per m²?

A hollow metallic cylindrical tank has an internal radius of 80 cm and height 200 cm. The thickness of the metal is 1 cm. If the tank is melted and cast into a right circular cone of height 3 m, find the radius of the cone, correct to two decimal places.

A hollow cylinder of internal and external radii 8 cm and 10 cm, respectively and height 5 cm is melted is recasted into small cones of base radius 3 cm and height 5 cm. Find the number of cones.

A solid cylinder is mounted with a hemispherical bowl of radius 5 cm (as shown in the figure). If the height of the whole solid portion is 28 cm. Find the volume of the whole solid. (Answer up to two decimal places.)

A hospital room is supposed to accommodate 56 patients. It should be done in such a way that every patient gets 2.2 m² of floor and 8.8 m³ of space. If the length of the room is 14 m, the breadth and the height of the room respectively are

The total surface area of a cylinder of height 8 cm is 528 cm². It is melted and recast into spheres of radius 2 cm. How many spheres can be obtained?

The volume of one sphere is 8 times that of another sphere. What will be the ratios of their radii and surface areas, respectively?

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

From a circle of radius 15 cm, a sector of angle 288° is cut out and its bounding radii are bent so as to form a cone. What is its approximate volume? (Take = 22/7)

A sphere completely fits into a cylinder as shown in the figure. What is the ratio of the curved surface area of cylinder to the surface area of sphere?

A cone is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.

A solid right circular cone of base diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, what is the internal diameter of the sphere?

An ice cream cone is packed full of ice cream and has a shape as depicted in the diagram. If the volume of ice cream inside the cone is the same as the volume of ice cream outside the cone, the height of the cone is

Water is pumped out through a cylindrical pipe of internal diameter 28 cm. How much water is pumped out in one hour if the flow velocity of water is 4 cm/s?

A cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 7 cm and height 5 cm is dropped into it. What is the rise in water level after it is completely immersed?

A solid vessel of cylindrical shape, having volume of 33.264 litres, is cast into a conical shape of height 72 cm. What is the cost of painting its CSA at Rs. 12 per sq. m?

In the following figure, two cones of the same radius are joined together as shown. Which of the following statements is definitely true regarding the figure?

The ratio of the radius of the base to the height of a cone is 5 : 12. If the cost of smoothening the curved surface area (CSA) is Rs. 115.50 at a rate of 5 paise per sq. cm, then what is the total surface area of the cone?

A sphere of diameter 6 cm is dropped into a right circular cylindrical vessel, partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

A cylinder, a hemisphere and a cone stand on the same base and have equal heights. The ratio of the areas of their curved surfaces is

A sphere with radius r is cut into two halves by a plane passing through the centre of the sphere. Two hemispheres of same radii are formed. Which of the following relations is true in this case?

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