A sheet music cabinet is 1.4m wide, 45 cm deep and 1.5m high. What is the surface area of the cabinet, not including the open front? Express your answer to the nearest tenth of a square metre.
To find the surface area of the cabinet, we need to calculate the area of each of its sides and then add them together.
First, let's break down the sides of the cabinet:
1. The top and bottom sides have the same dimensions, so we'll calculate the area of one side and then multiply it by 2.
Area of a rectangle = length × width
Area = 1.4 m × 45 cm
Note: We need to convert cm to meters to keep the units consistent.
1 cm = 0.01 m (since there are 100 cm in 1 m)
Area = 1.4 m × 0.45 m
Area = 0.63 m² (rounded to two decimal places)
2. The two shorter sides have the same dimensions, so we'll multiply the area of one side by 2.
Area = 45 cm × 1.5 m
Area = 0.675 m² (rounded to three decimal places)
3. The two longer sides have the same dimensions, so we'll multiply the area of one side by 2.
Area = 1.4 m × 1.5 m
Area = 2.1 m²
Now, we can calculate the surface area by adding the areas of all the sides:
Surface area = (2 × 0.63 m²) + (2 × 0.675 m²) + (2.1 m²)
Surface area = 1.26 m² + 1.35 m² + 2.1 m²
Surface area = 4.71 m²
Therefore, the surface area of the sheet music cabinet, not including the open front, is approximately 4.7 square meters.