Isosceles weight

A designer weight is made from a glass cube by cutting off a triangular prism with an isosceles right-triangle base, where the legs of the triangle are each half the length of the cube's edge. What percentage of the cube is removed when making the weight?

Final Answer:

p =  12.5 %

Step-by-step explanation:

$$\begin{gathered} S_1=a^2 \\ b=a/2 \\ {S}_2=\frac{b\cdot b}{2} \\ {S}_2=\frac{a/2\cdot a/2}{2}=\frac{1}{8}\cdot a^2=\frac{1}{8}\cdot S_1 \\ p=100\cdot \frac{S_2}{S_1} \\ p=100\cdot \frac{1/8\cdot S_1}{S_1} \\ p=100\cdot \frac{1}{8}=\frac{100\cdot 1}{8}=\frac{100}{8}=12.5\% \end{gathered}$$

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