Question

Mai has a dome paperweight that she can use as a magnifier. The paperweight is

shaped like a hemisphere made of solid glass, so she wants to design a box to keep it in
so it won't get broken. Her paperweight has a radius of 3 cm.
What should the dimensions of
the inside of box be so the box is
as small as possible?

Answer 1

6 x 6 x 3 cm

Explanation:

The base of the box needs to fit the base of the hemisphere.

The maximum width and length of the hemisphere is the diameter of the base of the hemisphere (which is circular)

Diameter of a circle = 2r

As the radius = 3 cm, the diameter = 2 x 3 = 6 cm

Therefore, the width and length of the box should both be 6cm

The height of the box needs to accommodate the height of the hemisphere. The height of the hemisphere is the radius, so the height of the box should be 3 cm.

Therefore, the dimensions of the box should be 6 x 6 x 3 cm