A conical glass holds 131 cubic centimeters of water. It has a height of 5 centimeters. The radius of the top of the glass is sqrt((m)/(5pi)) centimeters, where m is a constant. What is the value of m ?

Question

A conical glass holds 131 cubic centimeters of water. It has a height of 5 centimeters. The radius of the top of the glass is  sqrt((m)/(5pi)) centimeters, where  m is a constant. What is the value of  m ?

Bytelearn · Accepted Answer

Volume formula and given values: The volume of a cone is given by the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height. Given that the volume V is 131 cubic centimeters and the height h is 5 centimeters, we can substitute these values into the formula to find the radius r.Simplifying the equation: Substitute the given values into the volume formula: 131 = (1/3)πr^2(5). Simplify the equation by multiplying both sides by 3 to get rid of the fraction: 393 = πr^2(5).Isolating πr^2: Divide both sides of the equation by 5 to isolate πr^2: 393/5 = πr^2. Calculate 393/5 to get 78.6 = πr^2.Solving for r^2: Now, divide both sides by π to solve for r^2: 78.6/π = r^2. Calculate 78.6/π using a calculator to get r^2 ≈ 25.Equating r^2 to m/(5π): We are given that the radius r of the top of the glass is sqrt(m/(5π)) centimeters. Therefore, we can equate r^2 to m/(5π). So, m/(5π) = 25.Solving for m: Multiply both sides of the equation by 5π to solve for m: m = 25 * 5π. Calculate m to get m = 125π.

A conical glass holds $131$ cubic centimeters of water. It has a height of $5$ centimeters. The radius of the top of the glass is $\sqrt{\frac{m}{5 \pi}}$ centimeters, where $m$ is a constant. What is the value of $m$ ?

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A conical glass holds $131$ cubic centimeters of water. It has a height of $5$ centimeters. The radius of the top of the glass is $\sqrt{\frac{m}{5 \pi}}$ centimeters, where $m$ is a constant. What is the value of $m$ ?