A cylindrical cup is 8 centimeters in height. When filled to the very top, it holds 480 cubic centimeters of water What is the radius of the cup, rounded to the nearest tenth?Explain or show your reasoning. Enter your answers and your explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

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A cylindrical cup is 8 centimeters in height. When filled to the very top, it holds 480 cubic centimeters of water What is the radius of the cup, rounded to the nearest tenth?Explain or show your reasoning. Enter your answers and your explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Answer 1

### The radius of the cup is approximately 4.4 cm.

Answer 2

## Step1: Establish the formula ### The formula for the volume \( V \) of a cylinder is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. ## Step2: Plug in the known values ### Given the height \( h = 8 \) cm and the volume \( V = 480 \) cubic cm, substitute these values into the volume formula: \( 480 = \pi r^2 \times 8 \). ## Step3: Solve for \( r^2 \) ### Rearrange the equation to solve for \( r^2 \): \( r^2 = \frac{480}{8\pi} \). ### Simplify: \( r^2 = \frac{60}{\pi} \). ## Step4: Solve for \( r \) ### Take the square root of both sides to find \( r \): \( r = \sqrt{\frac{60}{\pi}} \). ### Calculate \( r \) using \( \pi \approx 3.14 \): \( r = \sqrt{\frac{60}{3.14}} \approx \sqrt{19.11} \approx 4.37 \). ## Step5: Round to the nearest tenth ### The radius rounded to the nearest tenth is \( 4.4 \) cm.

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