Chimenea Surface Area

Difficulty:
higher
Rating:
4-stars
GCSE Marks:
5-marks

GCSE Text:
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:

chimenea

Calculate the area of metal used to construct the chimenea, giving your answer in cm² and rounded to the nearest whole number.

Suggestions:
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?

Waffle Sharing

Difficulty:
higher
Rating:
5-stars
GCSE Marks:
4-marks

GCSE Text:
A family of 2 adults and 3 children need to share 3 waffles between them.

a)  What fraction of a waffle will each person receive if the waffles are shared equally between 5?

b)  The three children insist that their portion is provided in a single piece of waffle (no cuts). What will be the size of the reflex angle at the centre of each waffle for them to receive the correct amount in a single piece?

c)  The waffles each measure 9cm in diameter. What area of waffle does each person receive? Give your answer rounded to 1 d.p.

Suggestions:
This question works well as a consolidate to work on sectors of circles. Often the second question confuses students, so getting them to sketch a waffle generally helps to visualise what is being asked and clarifies the presence of a reflex and obtuse angle when cutting.  Students take 3-4 minutes to answer this question in full.

Teachers could extend the learning by considering:

  • The thickness of each waffle is 3mm, and 20% of each waffle is made from caramel filling. What volume of caramel will each person receive in their share?