Inflating Mattress

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

GCSE Text:
A new mattress arrives as a rolled up vacuum sealed cyclinder. The mattress is laid out flat as shown below, but air needs to be allowed into the packaging so it inflates to its final cuboid shape. As the mattress expands, the width and length won’t change, but the depth will increase significantly. The current depth is just 15% of the final depth of the mattress.

What is the difference in the finished volume of the mattress, and the volume of the cyclinder that was delivered?

Mattress Inflate

Suggestions:
This question stretches the most able GCSE students. For those that don’t know where to start, it is always useful to remind them that marks are awarded for part of the final answer even if not completed. As no formulae are given for a question like this, the question works well to consolidate volume learning.  Students take 3-4 minutes to answer this question in full.

Teachers could extend the learning by considering:

  • Express the inflated volume as a percentage of the packed volume

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?