Conversion and Combination of Solids

A solid metallic block of volume $2$ cubic metres is melted and recast into a rectangular bar of length $32$ metres having a square base. If the weight of the block is $160 \mathrm{kg}$ and the biggest cube is cut off from the bar then the weight of the cube is _____.

A cone is cut by a plane parallel to its base and the small cone that obtained is removed then the remaining part of the cone is

Volume of a hollow sphere is$\frac{11352}{7}{\text{cm}}^3$ . If the outer radius is $8\text{ cm}$, find the inner radius of the sphere. (Take$\frac{22}{7}$ ​)

 Find the volume of a sphere whose circumference is $144$ units?

Find the Total surface area of a hollow hemisphere whose outer and inner radii are given as  $4·2$ cm and$1·4$ cm respectively.

Find the curved surface area of a hollow hemisphere whose outer radii is $6·1$cm.

The radius of circular top and base of frustum are $5 \mathrm{cm}$ and $7 \mathrm{cm}$, respectively. If the height of frustum is $11 \mathrm{cm}$, then find the total surface area of frustum.

The radius of circular top and base of frustum are $7 \mathrm{cm}$ and $3 \mathrm{cm}$, respectively. If the slant height of frustum is $11 \mathrm{cm}$, then find the total surface area of frustum.

The radius of circular top and base of frustum are $7 \mathrm{cm}$ and $3 \mathrm{cm}$, respectively. If the slant height of frustum is $11 \mathrm{cm}$, then find the curved surface area of frustum.

An iron rod of diameter $1 \mathrm{cm}$ and length $8 \mathrm{cm}$ is drawn into a wire of length $18 \mathrm{m}$ of uniform thickness, then the radius of the wire will be :

If a cone of height $24 \mathrm{cm}$ and base $6 \mathrm{cm}$ melted and reshape into a sphere. Then what will be the total surface area of sphere

The slant height of a bucket is $26 \mathrm{cm}$. The diameter of upper and lower circular ends are $36 \mathrm{cm}$ and$16 \mathrm{cm}$ . The height of the bucket is

By melting a solid sphere of radius $5$cm a solid right circular cone of the same circular base is made. The height of the cone is

A conical vessel of radius $6 \mathrm{cm}$ and height $8 \mathrm{cm}$ is completely filled with water. A metal sphere is lowered into the water. The size of the sphere is such that when it touches the inner surface, it just gets immersed. Then, the fraction of water that overflows from the conical vessel is

A bucket is in the form of a frustum of a cone and it can holds $28.49$ litres of water. The radii of the top and bottom of the bucket are $28 \mathrm{cm}$ and $21 \mathrm{cm}$ respectively. Then slant height of the bucket is (use $\pi =\frac{22}{7}$)

A hollow right circular cylindrical copper pipe is $21 \mathrm{cm}$ long. Its outer and inner diameters are $10 \mathrm{cm}$ and $6 \mathrm{cm}$ respectively. If the volume of copper used in making pipe is $k {\mathrm{cm}}^3$ then find $k$.

Find the product of radii of the base of a frustum of a right cone if its lateral area is $323 cm²$, its slant height is $17 cm$, and its height is $8 cm$.
 

Given a frustum of a right cone with circumference of the bases as $4\pi$ сm and $16\pi$ cm. The height of the frustum of the cone is $8$ cm. Find its total surface area.

The outer radius of a hollow hemisphere is double the inner radius then the curved surface area is 

The outer radius of a hollow hemisphere is $14 \mathrm{cm}$ and the curved surface area of the hollow hemisphere is $924 {\mathrm{cm}}^2$. Find the inner radius of the hollow hemisphere.