A key-hole plate is made by fixing a semicircle on the top of a rectangle and then…
MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
A key-hole plate is made by fixing a semicircle on the top of a rectangle and then drilling a circular hole through the rectangle, as described below:
• Rectangle: width 12cm, height 18cm.
• Semicircle: diameter equal to the rectangle’s width, attached along the top.
• Circular hole: radius 3cm, centred on the rectangle’s mid-line 6cm above the base.
Answer the following:
(i) Find the area of the plate that remains after the hole is drilled. Give your answer in terms of π.
(ii) Determine the total length of the outer boundary of the plate, not counting the circumference of the drilled hole. Express your answer in terms of π.