Quantitative Reasoning Mensuration Test 5 Online

1. A solid cube with an edge of 10 cm is melted to from two equal cubes. The ratio of the edge of the smaller cube to the bigger cube is?

2. A cylinder 6 cm in diameter is partially filled with water. A sphere 3 cm in diameter is gently dropped into the cylinder. To what further height will the water in the cylinder rise?

3. An iron cube of size 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet be in the ratio 1:5, then the sides are?

4. The height of a bucket is 45 cm. The radii of the two circular ends are 28 cm and 7 cm respectively.The volume of the bucket is?

5. A right circular cone and a right circular cylinder have equal base and equal height. If radius of the base and the height, are in the ratio 5:12, then ratio of the total surface area of the cylinder to that of the cone is?

6. A cylinder bucket of height 36 cm and radius 21 cm is filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed. The height of the conical heap is 12 cm. The radius of the heap at the base is?

7. A cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, then find radius of the ice-cream cone.

8. A copper sphere is drawn into a cylindrical wire of 4 meters length. If the diameter of the sphere is ten times the diameter of the wire, then what is the radius of the sphere?

9. Let A be the area of a square inscribed in a circle of radius 'r' and let B be the area of a hexagon inscribed in the same circle. Then B/A equals

10. Three cubes with sides in the ratio 3:4:5 are melted to form a single cube whose diagonal is 12√3 cm. The sides of the cubes are?

11. ABCD is a parallelogram. P,Q,R and S are points on sides AB, BC, CD and DA respectively such that AP=DR. If the area of the parallelogram ABCD is 16 cm², then the area of the quadrilateral PQRS is?

12. An iron pipe 20 cm long has exterior diameter equal to 25 cm. If thickens of the pipe is 1 cm, the whole surface of the pipe is?

13. A large cube is formed from the material obtained by melting three smaller cubes of 3,4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

14. If the height, curved surface area and the volume of a cone are h, c and v respectively, then 3πvh² - c²h² + 9v² will be equal to

15. A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cones is 16 m above the ground. The area of the canvas required for the tent is?