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

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

Réitigh do h.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Cealaigh \pi ar an dá thaobh.

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

Méadaigh an dá thaobh den chothromóid faoi 3.

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

Tugann aon rud a roinntear ar a haon é féin.

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

Fairsingigh \left(175r\right)^{3}

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

Ríomh cumhacht 175 de 3 agus faigh 5359375.

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

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi 5359375r^{3}.

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

Má roinntear é faoi 5359375r^{3} cuirtear an iolrúchán faoi 5359375r^{3} ar ceal.

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

Roinn 4r^{3} faoi 5359375r^{3}.

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

Réitigh do r.

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