AC9M10M01Year 10MeasurementPractised on site

AC9M10M01 — Year 10 Measurement

Official Curriculum Content Description:

solve problems involving the surface area and volume of composite objects using appropriate units

Worked Examples (1)

Example 1Volume & Surface Area of Composite Solids

A building has the shape of a square prism (base

10\text{ m} \times 10\text{ m}

, height

15\text{ m}

) with a square pyramid roof of height

12\text{ m}

. Find the total volume of the building in

\text{m}^3

.Give your answer to 1 decimal place.

Common mistake: Using a full prism instead of 1/3 for the pyramid volume.

Correct Answer:

1900.0\text{ m}^3

Accepted: A unit is optional (m^3, m³, cu m all accepted).

Worked Solution:

1. Volume of rectangular prism:

V_{\text{prism}} = b^2 h = 10^2 \times 15 = 1500

(

1500\text{ m}^3

). 2. Volume of pyramid:

V_{\text{pyr}} = \frac{1}{3} b^2 h = \frac{1}{3} \times 10^2 \times 12 = 400

(

400\text{ m}^3

). 3. Total volume:

V_{\text{total}} = 1500 + 400 = 1900

(

1900\text{ m}^3

Work through unlimited interactive questions for this curriculum skill, with instant answers and step-by-step methods.