Mathematics 4024 · O Level · Surface area and volume

Surface area and volume — practice question

This cookery measuring spoon is made up of a hemispherical bowl and a handle. The bowl has an internal volume of $20\text{ cm}^3$, and the handle measures $5\text{ cm}$ in length.
(a(i))[2]

Determine the internal radius of the hemispherical bowl.

(a(ii))[2]

A geometrically similar spoon has a hemispherical bowl with an internal volume of $50\text{ cm}^3$. Determine the length of its handle.

(b)[3]

A metal kitchen strainer is made from an open hemisphere with radius $5.5\text{ cm}$. $50$ holes are punched through the curved surface. Suppose the metal removed for each hole is a circle of radius $1.5\text{ mm}$. Calculate the external surface area remaining.

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