Solve 4/3pir^3=h/3{left(1.75r/1right)}^3pi

$$\frac{ 4 }{ 3 } \pi { r }^{ 3 } = \frac{ h }{ 3 } { \left( \frac{ 1.75r }{ 1 } \right) }^{ 3 } \pi$$

Solve for h

$$\left\{\begin{matrix}\\h=\frac{256}{343}\approx 0.746355685\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

$$\frac{4}{3}r^{3}=\frac{h}{3}\times \left(\frac{1.75r}{1}\right)^{3}$$

Multiply both sides of the equation by 3.

$$4r^{3}=h\times \left(\frac{1.75r}{1}\right)^{3}$$

Anything divided by one gives itself.

$$4r^{3}=h\times \left(1.75r\right)^{3}$$

Expand \left(1.75r\right)^{3}.

$$4r^{3}=h\times 1.75^{3}r^{3}$$

Calculate 1.75 to the power of 3 and get 5.359375.

$$4r^{3}=h\times 5.359375r^{3}$$

Swap sides so that all variable terms are on the left hand side.

$$h\times 5.359375r^{3}=4r^{3}$$

The equation is in standard form.

$$\frac{343r^{3}}{64}h=4r^{3}$$

Divide both sides by 5.359375r^{3}.

$$\frac{64\times \frac{343r^{3}}{64}h}{343r^{3}}=\frac{64\times 4r^{3}}{343r^{3}}$$

Dividing by 5.359375r^{3} undoes the multiplication by 5.359375r^{3}.

$$h=\frac{64\times 4r^{3}}{343r^{3}}$$

Divide 4r^{3} by 5.359375r^{3}.

$$h=\frac{256}{343}$$

Solve for r

$$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&h=\frac{256}{343}\end{matrix}\right.$$