6. Given the volume and the radius, find the height of the cylinder. Use 3.14 for \( \pi \). \( r=6 \mathrm{in}, V=904.32 \mathrm{in}^{3} \) a 9 in b 8 in c 7 in d 10 in

To find the height of the cylinder, we can use the formula for the volume of a cylinder: \[ V = \pi r^2 h \] Given \( V = 904.32 \, \text{in}^3 \) and \( r = 6 \, \text{in} \), we substitute these values into the formula: \[ 904.32 = 3.14 \times (6)^2 \times h \] Calculating \( (6)^2 = 36 \): \[ 904.32 = 3.14 \times 36 \times h \] \[ 904.32 = 113.04 \times h \] To find \( h \), divide both sides by \( 113.04 \): \[ h = \frac{904.32}{113.04} \approx 8 \, \text{in} \] So, the height of the cylinder is 8 in. (b) Now you know the magic behind the volume of a cylinder! Did you know that cylinder designs have been important throughout history, from ancient Greek temples to modern skyscrapers? Engineers love utilizing cylinders for their strength and stability—just think of all those sturdy columns holding up our favorite buildings!