PERIMETER AREA AND VOLUME
TIP: When doing these sort of problems, remember:
1) Perimeter is always the total distance around something. e.g. the perimeter of a field is the distance you would walk if you walked once round the edges of the field. Perimeter is measured e.g. cm, m etc.
2) GCSE maths exams have a formulae sheet which includes some (but not all) formulae for calculating areas and volumes of various shapes. Check out what will be available on the formulae sheet for your exam. Sample formulae for 3d shapes can be found here.
3) Area is measured in e.g. cm2, m2 etc. - ALWAYS include the correct units at the end of your answer. Area of a rectangle is length x width. There are 2 dimensions here hence the units end up to the power 2.
4) Volume is measured in e.g. cm3, m3 etc. - ALWAYS include the correct units at the end of your answer. Volume of a box is its length x width x height. There are 3 dimensions here hence the units end up to the power 3.
5) Make sure that you know that the Circumference (fancy name for the perimeter) of a circle = 2pr and that the Area of a circle = pr2.
Solve the following:
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1. A shop sign is to be created with semi-circular ends as shown in the picture. The shop manager wants the sign to have a border which is made from flexible plastic.
a) What length of border will be required to go round the sign? b) If the border costs £9.99 per metre, how much will the border cost? c) The cost of the sign is £150. The shop manager will not be charged just for the cost of the sign and the border, VAT will be added to the total at 17.5%. How much will the shop manager have to pay for the completed sign in total? |
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2. The new "Clown's Ball" paperweight has just been designed. It will have the same dimensions as indicated in the diagram and it is planned to use glass (density 2.85 g/cm3) for the bulk of the cone and a copper ball (density 8.91 g/cm3) will be set in the glass cone.
a) Calculate the volume of the paperweight. b) Calculate the volume of the copper ball. c) Use your answers to a) and b) to calculate the total mass of the paperweight. |
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3. The underneath of an arch in a town's railway viaduct is to be sold for a company to use as storage space. Each end of the arch must be boarded up before the arch is sold to allow any damp areas to dry out. The top of the arch forms a semi-circle.
a) What is the total area of boarding required? b) When the arch space is sold the total volume must be indicated on the sales brochure. Calculate the total volume in m3 to 2 d.p.
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4. The diagram shows a hot water cylinder, which is made up from
a cylinder which is capped with a hemisphere. Calculate the maximum
volume of water that the cylinder can hold. Give your answer in litres
to 3 s.f.. |
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5. The diagram shows a section of a rocket firework. If this section
can be completely filled with gunpowder, what is the volume of gunpowder
required?
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6. A wheelchair ramp is to be constructed at the local town hall
with the dimensions as shown in the diagram. The ramp must be made
of solid concrete. What volume of concrete is required to make the
ramp?
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7. The "Peardrop" is part of a silver necklace, its
dimensions are shown in the diagram. What volume of silver is required
to make the "Peardrop"?
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8. The diagram shows the planned design of a washing machine button.
The button comprises of a hemisphere attached to a cuboid with relative
dimensions as shown in the diagram. a) Show that the volume of the button is: px3 + x2y
b) Calculate the volume when x = 2cm and y = 1cm.
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