A rectangular sheet of paper of size 11 cm × 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is: (a) 1 : 1 (b) 7 : 11 (c) 11 : 7 (d)

A hollow sphere of external diameter 10 cm and internal diameter 6 cm is melted and made into a solid right circular cone of height 8 cm. Find the radius of the cone so formed. (Use π = )

A solid wooden capsule consists of a cylindrical block and two hemispheres, as shown. Find the sum of the total surface areas of the three separate parts shown in Figure 2. The radius is 3.5 cm and the cylindrical block is 14 cm long. (Use )

A solid metallic cylinder is cut into two identical halves along its height. The diameter of the cylinder is 7 cm and the height is 10 cm. Find: (a) The total surface area of both the halves. (b) The total cost of painting the two halves at the rate of ₹30 per cm². (Use π = 22/7)

Oil is stored in a spherical vessel, occupying of its full capacity. The radius of the spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with radius 21 cm. Find the height of the oil in the cylindrical vessel, correct to the nearest centimetre. (Take π = )

A solid wooden toy is prepared by joining a cone, a cylinder and a sphere, as shown in the given diagram. The radius of each of the three solids is 7 cm and heights of each of the cone and the cylinder is 24 cm. Find : (a) the total surface area of the given solid. (b) the cost of painting the total surface at the rate of ₹ 0.50 per cm2.

The given figure shows an eye-drop bottle consisting of a hemispherical part and a cylindrical part, with a conical cap. The height of the cylindrical part and the height of the conical cap are each equal to the diameter, 7 cm. (a) Find the minimum height of a cylindrical box in which the bottle can be packed. (b) Find the volume of the liquid medicine that the bottle can contain. Use π = 22/7.

The volume of a cylinder of height 3 cm is 48π cm3. The radius of the cylinder is: (a) 48 cm (b) 16 cm (c) 4 cm (d) 24 cm

If the volumes of two spheres are in the ratio 27 : 64, then the ratio of their radii is: (a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height. If the radius of the cylinder is 14 cm, find the rise in the water level.

In the given figure, AOB is a right-angled triangle and C is the midpoint of the hypotenuse AB. If the coordinates of C are (x, y), the point equidistant from A, O and B is: (a) (x, y) (b) (y, x) (c) (x/2, y/2) (d) (2x/3, 2y/3)

Find the equation of a line whose y-intercept is 6 and is parallel to x-axis. (a) y = 6 (b) x = 6 (c) x + y = 6 (d) y − x = 6