61. A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is molted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes?
62. The volume of a solid right circular cylinder of height 8 cm is 392π cm3. Its curved surface area (in cm2) is:
63. A right angled sector of radius $$r$$ cm is rolled up into a cone in such a way that the two binding radii are joined together. Then the curved surface area of the cone is
64. If the radius of the base of a right circular cylinder is increased by 20% and the height is decreased by 30%, then what is the percentage increase/decrease in the volume?
65. The length of the largest possible rod that can be placed in a cubical room is 35√3 m. The surface area of the largest possible sphere that fit within the cubical room $$\left( {{\text{assuming }}\pi = \frac{{22}}{7}} \right)$$ (in sq. m) is
66. A sphere is placed in a cube so that it touches all the faces of the cube. If 'a' is the ratio of the volume of the cube to the volume of the sphere, and 'b' is the ratio of the surface area of the sphere to the surface area of the cube, then the value of ab is:
67. The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of the solid cylinder is
68. A 22.5 m high tent is in the shape of a frustum of a cone surmounted by a hemisphere. If the diameters of the upper and the lower circular ends of the frustum are 21 m and 39 m, respectively, then find the area of cloth (in m2) used to make the tent (ignoring the wastage). $$\left( {{\text{Use }}\pi = \frac{{22}}{7}} \right)$$
69. Assume that a drop of water is spherical and its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely. Then the height of the glass (in cm) is:
70. The radii of two circular faces of the frustum of a cone of height 21 cm are 3 cm and 2 cm respectively. What is the volume of the frustum of the cone in cm3 $$\left( {\pi = \frac{{22}}{7}} \right)?$$
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