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Stage 1 - Stage 3

Volume of Prisms II


Revision of Volume of Prisms

We have been learning about the volume of objects, particularly rectangular prisms, and then prisms more broadly.  

Volume of a Prism

$\text{Volume of any prism }=\text{Area of Base }\times\text{Height }$Volume of any prism =Area of Base ×Height

$V=A_b\times h$V=Ab×h

Units for Volume

It is probably worthwhile to remind ourselves of the units that are often used for calculations involving volume.

Units for Volume

cubic millimetres = mm3

(picture a cube with side lengths of 1 mm each - pretty small this one!)

cubic centimetres = cm3

(picture a cube with side lengths of 1 cm each - about the size of a dice)

cubic metres = m3 

(picture a cube with side lengths of 1 m each - what could be this big?)

AND to convert to capacity - 1cm3 = 1mL

Worked Examples

QUEstion 1

Find the volume of the figure shown.

A hexagonal prism is depicted and is cut in half horizontally to form two trapezium prisms. Both trapeziums are oriented in opposite direction to each other, sharing a common base (the shorter base) that measures 5 cm, indicated by a dashed line. Each trapezium has a longer parallel side opposite the shared base, measuring 14 cm, and two non-parallel sides that are not labeled. The distance between the parallel sides of each trapezium is marked as 7 cm. The length of the hexagonal prism perpendicular to the bases is measured 3 cm.

question 2

A hole is drilled through a rectangular box forming the solid shown. Find the volume of the solid correct to two decimal places.

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