Question

1 draw each of the following and hence find its surface area:
a an ice cube with sides 2.5 cm
b a block of cheese measuring 14 cm by 8 cm by 3 cm
c a wooden wedge with a 3 cm by 4 cm by 5 cm right - triangular cross - section and length 8 cm.

Explanation:

Step1: Surface area of cube

The formula for the surface area of a cube is \(S = 6s^{2}\), where \(s\) is the side length. Given \(s=2.5\ cm\).

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Step2: Surface area of rectangular prism

The formula for the surface area of a rectangular prism is \(S=2(lw + lh+wh)\), where \(l = 14\ cm\), \(w = 8\ cm\), \(h = 3\ cm\)

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Step3: Surface area of triangular prism

The formula for the surface area of a triangular prism is \(S=2\times(\text{area of base})+\text{perimeter of base}\times\text{length}\).
The area of the right - triangular base \(A=\frac{1}{2}\times3\times4 = 6\ cm^{2}\).
The perimeter of the base \(P=3 + 4+5=12\ cm\), and the length \(L = 8\ cm\)

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Answer:

a. The surface area of the ice cube is \(37.5\ cm^{2}\).
b. The surface area of the block of cheese is \(356\ cm^{2}\).
c. The surface area of the wooden wedge is \(108\ cm^{2}\).