Whakaoti i te 4/3pir^3=h/3{left(175r/1right)}^3pi

$$\frac{ 4 }{ 3 } \pi { r }^{ 3 } = \frac{ h }{ 3 } { \left( \frac{ 175r }{ 1 } \right) }^{ 3 } \pi$$

Whakaoti mō h

$$\left\{\begin{matrix}\\h=\frac{4}{5359375}\approx 0.000000746\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&r=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakakore te \pi ki ngā taha e rua.

$$\frac{4}{3}r^{3}=\frac{h}{3}\times \left(\frac{175r}{1}\right)^{3}$$

Whakareatia ngā taha e rua o te whārite ki te 3.

$$4r^{3}=h\times \left(\frac{175r}{1}\right)^{3}$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$4r^{3}=h\times \left(175r\right)^{3}$$

Whakarohaina te \left(175r\right)^{3}.

$$4r^{3}=h\times 175^{3}r^{3}$$

Tātaihia te 175 mā te pū o 3, kia riro ko 5359375.

$$4r^{3}=h\times 5359375r^{3}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$h\times 5359375r^{3}=4r^{3}$$

He hanga arowhānui tō te whārite.

$$5359375r^{3}h=4r^{3}$$

Whakawehea ngā taha e rua ki te 5359375r^{3}.

$$\frac{5359375r^{3}h}{5359375r^{3}}=\frac{4r^{3}}{5359375r^{3}}$$

Mā te whakawehe ki te 5359375r^{3} ka wetekia te whakareanga ki te 5359375r^{3}.

$$h=\frac{4r^{3}}{5359375r^{3}}$$

Whakawehe 4r^{3} ki te 5359375r^{3}.

$$h=\frac{4}{5359375}$$

Whakaoti mō r

$$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&h=\frac{4}{5359375}\end{matrix}\right.$$