Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 7.3

Find the circumference and area of the following figure. Give the answer as a multiple of $\mathrm{\pi }$.

Calculate the circumference of a circle of diameter $10 \mathrm{cm}$ as a multiple of $\mathrm{\pi }$.

A circle has a radius of $7 \mathrm{mm}$. What is its circumference? Give the answer as a multiple of $\mathrm{\pi }$.

What is the area of a circle of diameter $1.9 \mathrm{cm}$? Give the answer as a multiple of $\mathrm{\pi }$.

The radius of a semi-circle is $3 \mathrm{cm}$. What is the area of the semi-circle? Give the answer as a multiple of $\mathrm{\pi }$.

A circle of circumference $12\mathrm{\pi } \mathrm{cm}$ is precision cut from a metal square as shown.

What is the length of each side of the square?

A circle of circumference $12\mathrm{\pi } \mathrm{cm}$ is precision cut from a metal square as shown.

What area of metal is left once the circle has been cut from it? Give your answer in terms of $\mathrm{\pi }$.

The diagram shows two concentric circles. The inner circle has a circumference of $14\mathrm{\pi } \mathrm{mm}$. The outer circle has a radius of $9 \mathrm{mm}$. Determine the exact area of the shaded portion.