Solve 4/3pir^3=(h/3)(1.75r/2)^3

$$4 / 3 \pi r ^ { 3 } = ( h / 3 ) ( \frac { 1.75 r } { 2 } ) ^ { 3 }$$

Solve for h

$$\left\{\begin{matrix}\\h=\frac{2048\pi }{343}\approx 18.757964299\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$4\pi r^{3}=h\times \left(\frac{1.75r}{2}\right)^{3}$$

Divide 1.75r by 2 to get 0.875r.

$$4\pi r^{3}=h\times \left(0.875r\right)^{3}$$

Expand \left(0.875r\right)^{3}.

$$4\pi r^{3}=h\times 0.875^{3}r^{3}$$

Calculate 0.875 to the power of 3 and get 0.669921875.

$$4\pi r^{3}=h\times 0.669921875r^{3}$$

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

$$h\times 0.669921875r^{3}=4\pi r^{3}$$

The equation is in standard form.

$$\frac{343r^{3}}{512}h=4\pi r^{3}$$

Divide both sides by 0.669921875r^{3}.

$$\frac{512\times \frac{343r^{3}}{512}h}{343r^{3}}=\frac{512\times 4\pi r^{3}}{343r^{3}}$$

Dividing by 0.669921875r^{3} undoes the multiplication by 0.669921875r^{3}.

$$h=\frac{512\times 4\pi r^{3}}{343r^{3}}$$

Divide 4\pi r^{3} by 0.669921875r^{3}.

$$h=\frac{2048\pi }{343}$$

Solve for r

$$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&h=\frac{2048\pi }{343}\end{matrix}\right.$$