These two cones are mathematically similar.

Cone $A$ has volume $2000 {\mathrm{cm}}^3$. Calculate the volume of Cone $B$ in ${\mathrm{mm}}^3$.

Expalin why any two spheres are mathematically similar.

The volume of a sphere of radius $4 \mathrm{cm}$ is $268 {\mathrm{cm}}^3$ (to $3$ significant figures). Find the volume of a sphere of radius $8 \mathrm{cm}$.     [Enter the value excluding units]

The volume of a sphere of radius $4 \mathrm{cm}$ is $268 {\mathrm{cm}}^3$ (to $3$ significant figures). Find the volume of a sphere of radius $2 \mathrm{cm}$.     [Enter the value excluding units]

If the height of a cone is $k \mathrm{mm}$ that has volume $270\pi {\mathrm{mm}}^3$ and base radius $9 \mathrm{mm}$ then find the value of $k$.

If the radius of a cone is $k \mathrm{cm}$ that has volume $8.38 {\mathrm{cm}}^3$ and height $2 \mathrm{cm}$, then find the value of $k$. [Use $\mathrm{\pi }=3.14$ and round off up to two decimal places]

Find the radius of a sphere with volume $523.6 {\mathrm{cm}}^3$.

[Use $\mathrm{\pi }=3.14$ and write the value to the nearest integer excluding units]

Suppose you fill an empty sphere with water and then pour it into an empty cylinder that has the same height and diameter as the sphere. Find the height up the cylinder that the water would reach. Leave your answer as a fraction of the total height of the cylinder.

Find the surface area and volume of the following $3D$ solid.