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Measurement
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CanadaON
Grade 12

Further volumes of prisms

Lesson
Practice
Lesson

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 trapezoid prisms. Both trapezoids 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 trapezoid 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 trapezoid 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.

Outcomes

12C.C.1.3

Solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite figures, in situations arising from real-world applications

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