Volume, SM-Bank 016

A concrete staircase leading up to the grandstand has 10 steps.

The staircase is 1.6 m high and 3.0 m deep.

Its cross-section comprises identical rectangles.

One of these rectangles is shaded in the diagram below.

Find the area of the shaded rectangle in square metres. (2 marks)

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The concrete staircase is 2.5 m wide.

Find the volume of the solid concrete staircase in cubic metres. (2 marks)

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a. \(0.048\ \text{m}^2\)

b. \(6.6\ \text{m}^3\)

Show Worked Solution

a. \(\text{Height of rectangle}\)

\(=\dfrac{1.6}{10}\)

\(=0.16\ \text{m}\)

\(\text{Length of rectangle}\)

\(=\dfrac{3.0}{10}\)

\(= 0.3\ \text{m}\)

\(\therefore\ \text{Area of rectangle}\)	\(=0.16\times 0.3\)
	\(=0.048\ \text{m}^2\)

b. \(\text{55 rectangles make up the cross-section}:\)

\(\therefore\ A\)	\(=55\times 0.048\)
	\(= 2.64\ \text{m}^2\)