Manipur Board Solutions for Chapter: Mensuration, Exercise 3: EXERCISE 12.3

The radii of the top and bottom of a bucket are $21 \mathrm{cm}$ and $14 \mathrm{cm}$. Determine the capacity and curved surface area of the bucket if its height is $24 \mathrm{cm}$.

Rain water from a horizontal roof $11 \mathrm{m}\times 6 \mathrm{m}$ drains into a vessel in the form of a frustum of a cone. The height of the vessel is $1.4 \mathrm{m}$ and the radii of its top and bottom are $0.9 \mathrm{m}$ and $0.6 \mathrm{m}$. If the vessel is just full, find the rainfall in centimetres.

A solid cone of height $16.8 \mathrm{cm}$ and base radius $4.2 \mathrm{cm}$ is melted and recast into a solid sphere. Determine the radius of the sphere.

A solid sphere is melted and recast into a cone whose (base) radius is the same as that of the sphere. Show that the slant height of the cone bears a ratio $\sqrt{17}:4$ to its height.

A solid is in the form of a cone surmounted on a hemisphere of the same radius. If the height of the cone is $24 \mathrm{cm}$ and radius of the hemisphere is $7 \mathrm{cm}$, find the volume and surface area of the solid.

How many leads shots, each of radius $6 \mathrm{cm}$ can be made out of a rectangular slab of dimensions $44 \mathrm{cm}\times 36 \mathrm{cm}\times 24 \mathrm{cm}$?

Find the surface area and volume of a solid in the form of a right circular cylinder with hemispherical ends if the whole length is $22 \mathrm{cm}$ and radius of the cylinder is $3 \mathrm{cm}$.(Take $\mathrm{\pi }=3.14$)

A metallic right circular cylinder of radius $6 \mathrm{cm}$ and height $14 \mathrm{cm}$ is melted and recast into three spheres. If the radii of two of these spheres are $2 \mathrm{cm}$ and $3 \mathrm{cm}$, find the radius of the third.