Quantitative Reasoning Mensuration Test 4 Online

1. The radius of a Cylindrical cistern is 10 meters and its height is 15 meters. Initially the cistern is empty. We start filling the cistern with water through a pipe whose diameter is 50 cm. Water is coming out of the pipe with a velocity of 5 m/s. How many minutes will it take in filling the cistern with water?

2. What is the area of the inner equilateral triangle if the side of the outermost square is 'a'? (ABCD is a square)

3. A semicircular sheet of paper of diameter 28 cm is bent to cover the exterior surface of an open conical ice cream cup. The depth of the ice cream cup is?

4. A square and an equilateral triangle have the same perimeter. If the diagonal of the square is 12√2 cm, then the area of the triangle is?

5. If a solid sphere of radius 10 cm is molded into 8 spherical solid balls of equal radius, then the surface area of each ball is?

6. An edge of a cube measures 10 cm. If the largest possible cine is cut out of this cube, then volume of the cone is?

7. A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls. The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third ball is?

8. A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube

9. A sphere and a cube have the same surface area. The ratio of the volume of the sphere to that of the cube is?

10. A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel party filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely sumerged in water, by how much will the level of water rise in the cylindrical vessel?

11. A cone, a hemisphere and a cylinder have equal bases and same heights.Their volumes will be in the ratio

12. In the figure, ABCD is a square with side 10. BFD is an arc of a circle with center C. BGD is an are of a circle with center A. What is the area of the shaded region?

13. A rectangular carpet has an area of 60m². Its diagonal and longer side together equal 5 times the shorter side. The length of the carpet  is?

14. 2 cm of rain has fallen on a sq. km of land. Assuming that 50% of the raindrops could have been collected and contained in a pool having a 100m × 10 m base, by what level would the water level in the pool have increased?

15. A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is?