Mensuration Level-2 Quiz-1

1. A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder are equal to their diameters. Then their volumes are proportional, respectively, to?

2. A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and frustum are in the ratio?

3. The sides of a triangle are 5, 12 and 13 units respectively. A rectangle is constructed which is equal in area to the triangle and has a width of 10 units. Then the perimeter of the rectangle is?

4. From a circular sheet of paper with a radius 20 cm, four circles of radius 5cm each are cut out. What is the ratio of the uncut to the cut portion?

5. A closed wooden box of thickness 0.5 cm and length 21 cm, width 11 cm, and height 6 cm, is painted inside. The expenses of painting are Rs. 70. What is the rate of painting in rupees per sq. cm.?

6. Each side of a triangle is 6 cm less than the sum of the other two sides. The area of triangle = n*sqrt(3), Find n.

7. The length, the breadth and the height of a cuboid are in the ratio of 5 : 4 : 3. The longest rod that can be placed in the cuboid is 10 2 cm. What is the volume of the cuboid (in cm 3 )?

8. The perimeter of the sector of a circle of radius 14 cm is 41 cm. Find the area of the sector.

9. A cylindrical vessel having base radius 7 cm and height 6 cm is surmounted by a cone of height 24 cm. The curved surface area (in cm2) of the resultant solid is?

10. ABCD is a parallelogram having an area of 40Sqrt(3) sq.cm . E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Find the area (in sq. cm) of EFGH.