Question

1. here are the 6 views of an object made using centimetre cubes. determine its surface area.

top
left side front right side
bottom
back
a. ( 28 mathrm{~cm}^{2} ) b. ( 17 mathrm{~cm}^{2} ) c. ( 11 mathrm{~cm}^{2} ) d. ( 22 mathrm{~cm}^{2} )

Explanation:

Step1: Analyze each view's area contribution

Each centimetre cube has a face area of \(1 \, \text{cm}^2\) (since side length is \(1 \, \text{cm}\), area of one face is \(1\times1 = 1 \, \text{cm}^2\)).

• Top and Bottom: Both have 3 squares. So total for top + bottom: \(2\times3 = 6 \, \text{cm}^2\).
• Left and Right sides: Both have 3 squares. Total for left + right: \(2\times3 = 6 \, \text{cm}^2\).
• Front and Back: The front (and back) has a cross - like shape. Let's count the squares: the front has 5 squares (the cross: 3 in the middle row, 1 above, 1 below). So front + back: \(2\times5 = 10 \, \text{cm}^2\).

Step2: Sum up all areas

Now, add the areas from each pair of views:
Total surface area \(= 6 + 6 + 10 = 22 \, \text{cm}^2\).

Answer:

d. \(22 \, \text{cm}^2\)