Mensuration Level-2 Quiz-2

1. The radius of a cylindrical box is 14 cm and its height is 9 cm. By decreasing the height or radius by x cm, the decrease in volume is the same. What is the value of x? (given that, x ≠ 0)

2. The total surface area of a cuboid is 280 sq. cm. The areas of two of its adjacent surfaces are 72 sq. cm and 36 sq. cm. Find the length of the cuboid if it is the greatest of the dimensions.

3. An equilateral triangle is inscribed in a circle of radius 8 cm and another equilateral triangle is circumscribed about the circle. Find the difference between the areas of the two triangles is n*sqrt(3). Find n.

4. The length and the breadth of a cuboid are increased by one-eighth and one-third respectively. What should be the percentage increase in the height such that the volume which was 150 cu. cm earlier, becomes 300 cu. cm?

5. A lawn mower is in the shape of a cylinder. The radius of cross-section is 14 cm and the length is 1 m. What is the area covered by the lawn mower in making 200 revolutions? (in m^2 )

6. The sum of perimeters of an equilateral triangle and a rectangle is 90 cm. The area, T, of the triangle and the area , R, of the rectangle, both in sq cm, satisfy the relationship R = T². If the sides of the rectangle are in the ratio 1 : 3, then the length, in cm, of the longer side of the rectangle, is?

7. The length, the breadth and the height of a cuboid are in the ratio 6 : 5 : 4. If the length was 20% more, the breadth was 25% more and the height was 25% less, then the total surface area of the cuboid would have been approximately?

8. What is the circumradius of the triangle whose sides are 102.6 cm, 136.8 cm and 171 cm?(in cm)

9. Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps : the original square of side a is divided into n smaller squares, not necessarily of the same size ; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is?

10. There are two tanks, one cylindrical and the other conical. The cylindrical tank contains 500 liters Limca more than the conical tank. 200 liters is removed both from the cylindrical and conical tank. Now the cylindrical tank contains double the volume of liquid in the conical tank. What is the capacity of the cylindrical tank in liters?