Abhijit Guha Solutions for Chapter: Volume and Surface Area of Solid Figures, Exercise 3: Exam Problems

The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube will be:

A school room is to be built to accommodate $70$ children so as to allow $2.2{\mathrm{m}}^2$ of floor and $11{\mathrm{m}}^3$ of space for each child . If the room be $14\mathrm{m}$ long, what must be its breadth and height?

The radii of the base of a cylinder and a cone are in the ratio $\sqrt{3}:\sqrt{2}$  and their heights are in the ratio  $\sqrt{2}:\sqrt{3}$ Their volume are in the ratio of:

A cone of height$7 \mathrm{cm}$ and base radius $1 \mathrm{cm}$ is carved from a cuboidal block of wood $10 \mathrm{cm}\times 5\mathrm{cm}\times 2\mathrm{cm}$. Assuming $\pi =\frac{22}{7}$, the percentage wood wasted in the process is _____

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then:

A solid spherical copper ball whose diameter is $14 \mathrm{cm}$ is melted and converted into a wire having diameter equal to $14 \mathrm{cm}$. The length of the wire is:

Diagonal of a cube is $6\sqrt{3} \mathrm{cm}$. Ratio of its total surface area and volume (numerically) is:

The Volumes of a right circular cylinder and a sphere are equal. The radius of the cylinder and the diameter of the sphere are equal. The ratio of height and radius of the cylinder is _____.