1. The base of a right prism is a quadrilateral ABCD, given that AB = 9 cm, BC = 14 cm, CD = 13 cm, DA = 12 cm and ∠DAB = 90°. If the volume of the prism be 2070 cm3, then the area of the lateral surface is
2. The circumference of the base of a right circular cone is 44 cm and its height is 24 cm. The curved surface area (in cm2) of the cone is:
3. The height of a circular cylinder is increased six times and the base area is decreased to one ninth of its value. The factor by which the lateral surface of the cylinder increases is
4. If a solid cone of volume 27π cm3 is kept inside a hollow cylinder whose radius and height are equal to that of the cone, then the volume of water needed to fill the empty space is
5. The volume of a conical tent is 1232 m3 and the area of its base is 154 sq. m. Find the length of the canvas required to build the tent, if the canvas is 2 m in width. $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
6. A spherical metallic shell with 6 cm external radius weight 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm3?
7. If 3.96 cubic dm of lead is to be drawn into a cylindrical wire of diameter 0.6 cm, then the length of the wire (in metres), is:
8. A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube?
9. The radius of a sphere is reduced by 40%. By what percent will its volume decrease?
10. The radius of the base of a right circular cylinder is increased by 20%. By what per cent should its height be reduced so that its volume remains the same as before?
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