Question

8 a rectangular garage floor 9.2 m by 6.5 m is to be concreted to a depth of 120 mm.
a what volume of concrete is required?
b concrete costs €135 per m³, and is only supplied in multiples of 0.2 m³. how much will it cost to concrete the floor?

Explanation:

Part (a)

Step 1: Convert depth to meters

The depth is 120 mm. Since 1 m = 1000 mm, we convert 120 mm to meters by dividing by 1000: \( 120\div1000 = 0.12\) m.

Step 2: Calculate volume of rectangular prism

The volume \( V \) of a rectangular prism (which the concrete forms) is given by \( V=\text{length}\times\text{width}\times\text{height (depth)} \). Here, length = 9.2 m, width = 6.5 m, depth = 0.12 m. So \( V = 9.2\times6.5\times0.12 \). First, calculate \( 9.2\times6.5 = 59.8 \). Then, \( 59.8\times0.12 = 7.176 \) \( \text{m}^3 \).

Step 1: Determine the amount of concrete to buy

The volume needed is \( 7.176\space \text{m}^3 \), and concrete is supplied in multiples of \( 0.2\space \text{m}^3 \). We divide \( 7.176\) by \( 0.2 \): \( 7.176\div0.2 = 35.88 \). Since we can't buy a fraction of a multiple, we need to round up to the next whole number of multiples. So we need \( 36\times0.2 = 7.2\space \text{m}^3 \) (because 35 multiples would be \( 35\times0.2 = 7.0\space \text{m}^3 \), which is less than 7.176, so we need 36 multiples).

Step 2: Calculate the cost

The cost per \( \text{m}^3 \) is €135. So the total cost is \( 7.2\times135 \). Calculate \( 7\times135 = 945 \) and \( 0.2\times135 = 27 \), then add them: \( 945 + 27 = 972 \) euros.

Answer:

The volume of concrete required is \( 7.176\space \text{m}^3 \).

Part (b)