AREA OF A CIRCLE WORD PROBLEMS WORKSHEET

Problem 1 :

The inner part of an athletics track is lawn. Find the area of the lawn.

Solution

Example 2 :

A door has the dimensions shown.

(a)  How high is the door at its highest point ?

(b)  What is the area of the door in square meters ?

Solution

Example 3 :

Find the area of the shaded region.

Solution

Example 4  :

A circular table top has a diameter of 1.6 m. A rectangular tablecloth 2 m by 2 m is placed over the table top. What area of the tablecloth overlaps the table ?

Solution

Example 5 :

Consider a square within a circle. 

(a)  Find the area of:

i) the circle

ii) the shaded triangle

iii) the square.

(b) What percentage of the circle is occupied by the square ?

Solution

Example 6 :

(a)  Find the shaded area.

(b) Find the sum of the perimeters of the two circles.

Solution

Example 7 :

A circular rug is laid on a tiled floor. Find

a) the area of the rug

b) the visible area of the tiled floor.

Solution

Example 8 :

A gardener is making a path using 8 cylindrical concrete pavers. Each paver has a radius of 20 cm and is 5 cm thick.

(a)  Find the total area of the tops of the pavers.

(b)  Find the total volume of the pavers

Solution

Problem 1 :

A cylindrical tank has radius 1.5 m. What is the circumference of its base ?

Solution

Problem 2 :

A circular pond has diameter 8 m and needs to be fenced for the protection of children.

a) What length of fencing is required?

b) Fencing comes in 1 m lengths. How many lengths are needed?

c) What is the total cost of the fencing if each length costs $25.00?

Solution

Problem 3 :

A car wheel has a radius of 35 cm.

a)  What is the circumference of the wheel?

b)  If the wheel rotates 100 000 times, how far does the car travel?

Solution

Problem 4 :

A trundle wheel is used for measuring distances. The circumference of the wheel is exactly 1 m. Each time the wheel rotates through one complete turn a click sound is heard and a counter adds a meter to the total. What is the radius of this wheel

Solution

Problem 5 :

A circular garden plot has circumference 12.65 m. Find its radius in meters, correct to the nearest centimetre.

Solution

Problem 6 :

An irrigation sprinkler sprays water over a field. The radius of the spray is 12.6 m. What area of the field is being watered?

Solution

Problem 7 :

The rope connecting a goat to a pole is 8 m long. What area of grass can the goat eat?

Solution

Problem 8 :

A circular hoop has a radius of 40 cm. Find the length of tubing needed to make the hoop.

Solution

Problem 9 :

6 identical metal discs are stamped out of an 18 cm by 12 cm sheet of copper as illustrated. What percentage of the copper is wasted

Solution

Problem 10 :

A table-top is shaped as illustrated. A cloth to protect the table-top from stains and heat is cut exactly the same size as the table-top. It is made from fabric 1.6 m wide and costs $18.40 per metre of length.

a) What length of fabric must be purchased?

b) Calculate the cost of the fabric.

c) Find the area of the cloth.

d) Calculate the amount of fabric that is wasted.

Solution

Problem 11 :

A circular mat has a diameter of 53 centimeters. Lily wants to sew a decorative braid around the mat. How many centimeters of braid does she need? Give your answer to the nearest tenth of a centimeter. Use 3.14 as an approximation of π.

Solution

Problem 12 :

A metalworker cuts out a large semicircle with a diameter of 28 centimeters. Then the metalworker cuts a smaller semicircle out of the larger one and removes it. The diameter of the semicircular piece that is removed is 14 centimeters. Find the distance around the shape after the smaller semicircle is removed. Use 22/7 as an approximation for π.

Solution

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