**1.A cylindrical can whose base is horizontal and is of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed inside, water just covers the sphere. The sphere fits in the can exactly. The depth of water in the can before the sphere was put is**

**2.The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq. com) of the triangle 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.The volume of a right circular cone is 1232 cm^3 and its vertical height is 24 cm. Its curved surface area is**

**5.A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is.**

**6.The area of a circle is increased by 22 cm^2 when its radius is increased by 1 cm. The original radius of the circle is**

**7.The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is**

**8.The height of a right prism with a square base is 15 cm. If the area of the total surfaces of the prism is 608 sq. cm, its volume is**

**9.If the diagonals of a rhombus are 8 and 6, then the square of its size is**

**10.The volume of a solid hemisphere a 19404 cm^3. Its total surface area is**

Answers and Solution:

1. (3) Increase in water level = volume of sphere/Area of base of cylinder

(4/3πr^3)/(πr^2)

= 4/3 r = 4/3*3.5 = 14/3 cm

so Required water level = 7 – 14/3 => 7/3 cm

2. (2)

3. (1)

Curved Surface area of cylinder = 2πrh

case II

Radius = 1/3r:height = 6h

curved surface = 2π*1/3*r*6h = (2πrh)*2

so increase will be twice.

4. (2)

5. (4)

2πr = 2(18+26)

=> 2 *22/7*r = 44*2

r = 14 cm

Area of circle = 616 sq.m

6.(1)

7. (4)

8. (3)

9. (1)

10. (1)

2/3 πr^3 = 19404

=> 2/3*22/7*r^3 = 19404

r = 21 cm

so Total surface area = 3πr^2

= 3*22/7*21*21 = 4158.sq.cm.