This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Sunday, November 18, 2007

Catholic High School 2006 PSLE Math Prelim Question

The figure below, not shown to scale, is made up of semi-circles and circles. Given that the diameter of the large semicircle is 42 cm, find the area of the shaded region and express your answer as a fraction in the lowest term.


Area of large semi-circle

1/2 x (22/7) x 21cm x 21cm = 693 square cm

Area of 1 circle (within large semi-circle)

(22/7) x 7cm x 7cm = 154 square cm

Note -
Radius of circle is 7cm because diameter of large semi-circle is 42cm. This diameter is equivalent to the total diameters of the 3 smaller semi-circles at the base of the figure above. Diameter of 1 small semi-circle is therefore 42cm divided by 3 = 14cm. Radius of smaller semi-circle (and circle) is hence, 7 cm.

There are 2 circles and 3 smaller semi-circles in the large semi-circle. This is equivalent to an area of 3.5 circles within the large semi-circle. Therefore,

Area of 3.5 circles (within large semi-circle) is

154 square cm x 3.5 = 539 square cm.

Area of the portion that is inside large semi-circle, but outside the two circles and three small semi-circles is

693 square cm - 539 square cm = 153 square cm

Area of shaded portion is 1/3 the area above, therefore,

154 square cm divided by 3
= 51 and 1/3 square cm (Answer)

No comments: