Exact Values (Edexcel GCSE Maths: Foundation)

Triangle  is a right-angled triangle.

.
.

Work out the length .
Give your answer as an exact value.

is a square.
All shapes within  are also squares.

What fraction of the square is shaded?

A cylinder has a radius of 4 cm and a height of 7 cm.  

Find the volume of the cylinder.
Leave your answer in terms of .

...................................... cm³

Here is a quarter circle of radius 6 cm

Work out the area of the quarter circle.
Give your answer in terms of .

............................cm²

A circular table top has radius 70 cm.

Calculate the area of the table top in cm², giving your answer as a multiple of.

....................... cm² 

Triangle  has perimeter  cm.

.
.

By calculation, deduce whether triangle is a right-angled triangle.

The diagram shows two identical circles of diameter 4 cm inside another circle.

The two identical circles both touch the circumference of the larger circle and meet at its centre.

Frances says that exactly  of the diagram is shaded. Is she correct?
You must show all your working.

The centimetre grid shows the plan and elevation of a cylinder.
1 square length on the grid represents 1 cm.

Work out the volume of the cylinder.
Give your answer in terms of .

................................... cm³

The diagram shows a circle drawn inside a square.

The circle has a radius of 6 cm.
The square has a side of length 12 cm.

Work out the shaded area.
Give your answer in terms of .

The diagram shows a circle inside a square.

 is a square of side 10cm.
Each side of the square is a tangent to the circle.

Work out the total area of the shaded regions in terms of .
Give your answer in its simplest form.

Here is a circle touching a square.

The area of the square is 64 cm²

Work out the area of the circle.

Give your answer in terms of .

........................................ cm²