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Grade 12

Volume of right prisms

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 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 cube shown.

A three-dimensional cube with edges depicted in a green outline. The front bottom edge of the cube is labeled with the measurement of $12$12 cm.

QUESTION 2

Find the volume of the rectangular prism shown.

A three-dimensional rectangular prism is depicted with its dimensions labeled. The height is labeled as 3 cm, the width as 2 cm, and the length as 8 cm.

QUESTION 3

Find the volume of the prism by finding the base area first.

A three-dimensional trapezoid prism is depicted. The trapezoid is facing front. The trapezoid has a bottom base measuring 16 cm, and a top base measuring 13 cm. The height of the trapezoid is measured 5 cm. The depth of the shape is measured 3 cm.

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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