# Module 4 - Unit 4: Circles and Cylinders

## Self-Audit

For the multiple choice questions below, choose one answer, (a), (b), (c) or (d), that is CORRECT by clicking the appropriate box.
Calculators are NOT allowed unless it is indicated in the question.
You will need a pair of compasses, a ruler, a pertractor, some paper and some string in order to answer some of these questions.

## Section 4.1 - Introduction to Circles

Question 1
 What is the name given to a chord of a circle that passes through the centre of the circle? (A) Radius   (B) Arc (C) Diameter (D) None of these
Question 2
 The diagram shows a triangle drawn inside a circle of radius 5 cm. The line AB is a diameter of the circle. Draw the triangle accurately nad use it to answer the next three questions. What is the length of AC? (A) 5 cm   (B) 6 cm (C) 7 cm (D) None of these
Question 3
 For the triangle you drew in Question 2, what is the size of the angle ACB? (A) 60°   (B) 80° (C) 90° (D) None of these
Question 4
 What is the area of the triangle in Question 2? (A) 24 cm2   (B) 36 cm2 (C) 48 cm2 (D) None of these

## Section 4.2 - Estimating the Circumference of a Circle

Question 5
 What is the name given to the perimeter length of a circle? (A) Circumference   (B) Area (C) Sector (D) None of these
Question 6
 Draw a circle of radius 4 cm and use string to measure the length of its circumference. Approximately what is the length of the circumference? (A) 20 cm   (B) 25 cm (C) 30 cm (D) 40 cm
Question 7
 Draw a circle of radius 5 cm and measure the length of its circumference. Approximately what is the length of the circumference? (A) 25 cm   (B) 30 cm (C) 40 cm (D) 50 cm
Question 8
 Using your answers to Questions 6 and 7, what approximately is the ratio of a circle's diameter to its circumference? (A) 1 : 1   (B) 2 : 1 (C) 3 : 1 (D) 4 : 1

## Section 4.3 - Estimating the Area of a Circle

Question 9
 Draw a circle of radius 4 cm onto 1 cm2 squared paper. Estimate its area. (A) 30 cm2   (B) 40 cm2 (C) 50 cm2 (D) 60 cm2
Question 10
 From your answer to Question 9, what is the ratio of a circle's radius squared to its area? (A) 2 : 1   (B) 3 : 1 (C) 4 : 1 (D) 5 : 1
Question 11
 Draw a semi-circle of radius 5 cm onto 1 cm2 squared paper. Estimate the area of this semi-circle. (A) 36 cm2   (B) 40 cm2 (C) 50 cm2 (D) 60 cm2
Question 12
 From your answer to Question 11, what is the ratio of a semi-circle's radius squared to its area? (A) 1.5 : 1   (B) 2.0 : 1 (C) 2.5 : 1 (D) None of these

## Section 4.4 - Formulae for Circumference and Area

Question 13
 A circle has radius 7 cm. What is the length of its circumference, to the nearest cm? (A) 22 cm   (B) 43 cm (C) 44 cm (D) None of these
Question 14
 What is the area of the circle in Question 13 to the nearest cm2? (A) 21 cm2   (B) 44 cm2 (C) 154 cm2 (D) None of these
Question 15
 A circle has circumference of length 37.7 cm. What is the length of its diameter to the nearest cm? (A) 12 cm   (B) 6 cm (C) 3 cm (D) None of these
Question 16
 The area of a circle is 201 cm2. What is the length of its radius to the nearest cm? (A) 4 cm   (B) 8 cm (C) 12 cm (D) None of these

## Section 4.5 - Problems in Context

This is a sketch of a garden. Question 17
 What is the length of the garden's perimeter, to one decimal place? (A) 6.3 m   (B) 16.3 m (C) 22.6 m (D) None of these
Question 18
 What is the area of the garden, to the nearest m2? (A) 6 m2   (B) 13 m2 (C) 18 m2 (D) None of these
This is a diagram of a shape. Question 19
 What is the circumference, to the nearest 1 decimal place, of the shape? (A) 3.1 m   (B) 7.1 m (C) 8.2 m (D) None of these
Question 20
 What is the area of the shape, to 2 decimal places? (A) 1.21 m2   (B) 1.57 m2 (C) 1.79 m2 (D) None of these

## Section 4.6 - Volume and Surface Area of a Cylinder

This diagram shows a cylinder. Question 21
 What is the volume of the cylinder? (A) 36π cm3   (B) 48π cm3 (C) 96π cm3 (D) None of these
Question 22
 What is the area of its curved surface? (A) 24π cm2   (B) 36π cm2 (C) 48π cm2 (D) None of these
Question 23
 What is the total surface area of the cylinder? (A) 18π cm2   (B) 33π cm2 (C) 42π cm2 (D) None of these
Question 24
 A cylinder has volume 200 cm3 and base radius 5 cm. What is the height, to 1 decimal place, of this cylinder? (A) 1.6 cm   (B) 2.5 cm (C) 12.7 cm (D) None of these Mark your answers.