Mensuration-3D || 15.03.2023

A solid metallic sphere of radius 8.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height of the cylinder? (Your answer should be correct to one decimal place.)

The radii of two right circular cylinders are in the ratio 3 : 2 and the ratio of their volumes is 27 : 16. What is the ratio of their heights?

A metallic sphere of radius 25 cm is melted into small spheres of diameter 1 cm. How many such small spheres can be made from the large sphere?

The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm²) of the remaining solid?

The curved surface area of a cylinder is 25344 cm and its height is 32 cm. What is the volume of a cylinder whose capacity is  times the volume of the given cylinder?

A hemispherical vessel of internal radius 15 cm is full of a liquid. This vessel is to be emptied by a cylindrical bottle of radius 3 cm and height 10 cm. How many such bottles are required to empty the bowl?

The edge of a cube is 8 cm. What is the total surface area of the cube?

15 cylindrical containers each of radius of 3.5 cm and height 20 cm are placed together in a cuboidal box as shown in the figure. What is the volume of the empty space which is formed inside the box?

The volume of a right circular cylinder is 3 times the volume of a right circular cone. The radius of the cone and the cylinder are 3 cm ad 6 cm respectively. If the height of the cylinder is 1 cm, then what is the slant height of the cone?