A garden chimenea is made from a frustum with a circular base and a cylindrical chimney on the top. The legs are made from metal cut from the opening in the front. Here is the design for the chimenea body:
Calculate the area of metal used to construct the chimenea, giving your answer in cm² and rounded to the nearest whole number.
This question stretches the most able GCSE students. Many students assume that some measurements are missing (they’re not), and often benefit from drawing the frustum as two separate cones. Students can be confident of being given the formula for the curved surface area of a cone in a GCSE exam. This question is a good consolidator once students have learned cones, cylinders and similar shapes. Students take 5-6 minutes to answer this question in full.
Teachers could extend the learning by considering:
- A smaller chimenea is on offer where all measurements in the diagram are 10% less. By what percentage will the area of metal be reduced?