Seán has built a shed - Leaving Cert Mathematics - Question 9 - 2022

To find the volume of the shed, we first calculate the area of the face:

• The front face is a combination of a triangle and a rectangle.
• The area of the rectangle is given by length × width:

$Area_{rectangle} = 12 imes 5 = 60 ext{ m}^2$

• The area of the triangle is given by:

$Area_{triangle} = \frac{1}{2} \times base \times height = \frac{1}{2} \times 7 \times 8.5 = 29.75 ext{ m}^2$

Thus, the total area of the face of the shed is:

$Total \, Area = Area_{rectangle} + Area_{triangle} = 60 + 29.75 = 89.75 ext{ m}^2$

Now, we find the volume by multiplying the total area by the length of the shed:

$Volume = Total \, Area \times Height = 89.75 \times 18 = 1615.5 ext{ m}^3$

To convert this to litres:

$Volume_{litres} = 1615.5 imes 1000 = 1615500 ext{ litres}$

Since 1615500 litres is more than one million litres, Seán is correct.