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Question Number 186337 by normans last updated on 03/Feb/23

Commented by normans last updated on 03/Feb/23

$$\mathit{t}\mathit{h}\mathit{e}\mathit{v}\mathit{o}\mathit{l}\mathit{u}\mathit{m}\mathit{e}\mathit{o}\mathit{f}\mathit{t}\mathit{h}\mathit{e}\mathit{c}\mathit{u}\mathit{b}\mathit{e}\mathit{i}\mathit{s}300$$$$\mathit{t}\mathit{h}\mathit{e}\mathit{c}\mathit{u}\mathit{b}\mathit{e}\mathit{i}\mathit{s}\mathit{c}\mathit{u}\mathit{t}\mathit{w}\mathit{i}\mathit{t}\mathit{h}\mathit{a}\mathit{p}\mathit{l}\mathit{a}\mathit{n}\mathit{e}.$$$$\mathit{t}\mathit{h}\mathit{e}\mathit{v}\mathit{o}\mathit{l}\mathit{u}\mathit{m}\mathit{e}\mathit{o}\mathit{f}\mathit{t}\mathit{h}\mathit{e}\mathit{c}\mathit{u}\mathit{t}\mathit{p}\mathit{a}\mathit{r}\mathit{t}????$$

Answered by mr W last updated on 03/Feb/23

Commented by mr W last updated on 03/Feb/23

$$a=edgelengthofcube$$$$volumeofcubeV=a^3=300$$$$\frac{b}{a}=\frac{0.4a}{0.5a}$$$$\Rightarrow b=0.8a$$$$\frac{h}{h+a}=\frac{0.4a}{0.5a}=0.8$$$$\Rightarrow h=4a$$$$V_{cut}=V_1+V_2$$$$V_1=\frac{0.4a\times 0.8a}{2}\times \frac{a}{3}=\frac{4a^3}{75}$$$$V_2=\frac{(0.4a+0.5a)\times a}{2}\times \frac{a}{3}=\frac{3a^3}{20}$$$$V_{cut}=\frac{4a^3}{75}+\frac{3a^3}{20}=\frac{61a^3}{300}=\frac{61V}{300}=61✓$$$$or$$$$V_{cut}=\frac{0.5a\times a}{2}\times \frac{4a+a}{3}-\frac{0.4a\times 0.8a}{2}\times \frac{4a}{3}$$$$=\frac{61a^3}{300}=\frac{61V}{300}=61✓$$

Commented by normans last updated on 03/Feb/23

$$\mathit{n}\mathit{i}\mathit{c}\mathit{e}\mathit{S}\mathit{i}\mathit{r}$$

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