Final answer:
To find the radius of a sphere with a given volume and height, use the formula V = (4/3)πr^3 and rearrange to solve for r. Substitute the given volume and evaluate to find the radius.
Step-by-step explanation:
To find the radius of a sphere with a given volume and height, we need to use the formula for the volume of a sphere: V = (4/3)πr^3. Given that the volume V is 112 cm^3, we can rearrange the formula to solve for the radius r. Divide both sides of the equation by (4/3)π to isolate r: r^3 = V / ((4/3)π). An algebraic expression is an expression involving numbers, parentheses, operation signs, and pronumerals Substitute the given volume value and simplify: r^3 = 112 / ((4/3)π). Take the cube root of both sides to solve for r: r = (112 / ((4/3)π))^(1/3). Using this formula and evaluating it, we find that the radius of the sphere is approximately 2 cm.