10. The Da Silvas installed a cylindrical water heater with a radius of $30 \mathrm{~cm}$ and a height of $120 \mathrm{~cm}$.
(a) What is the surface area of the water heater?
(b) What is the volume of the water heater?
Answer
Final Answer: The surface area of the water heater is \(\boxed{28274.33 \, \text{cm}^2}\) and the volume of the water heater is \(\boxed{339292.01 \, \text{cm}^3}\).
Step 1 ：We are given a cylindrical water heater with a radius of 30 cm and a height of 120 cm.
Step 2 ：We need to find the surface area and volume of the water heater.
Step 3 ：The formula for the surface area of a cylinder is \(2\pi r(h + r)\), where \(r\) is the radius and \(h\) is the height.
Step 4 ：Substituting the given values into the formula, we get \(2\pi \times 30(120 + 30)\).
Step 5 ：Solving this, we find that the surface area of the water heater is approximately 28274.33 cm².
Step 6 ：The formula for the volume of a cylinder is \(\pi r^2h\), where \(r\) is the radius and \(h\) is the height.
Step 7 ：Substituting the given values into the formula, we get \(\pi \times 30^2 \times 120\).
Step 8 ：Solving this, we find that the volume of the water heater is approximately 339292.01 cm³.
Step 9 ：Final Answer: The surface area of the water heater is \(\boxed{28274.33 \, \text{cm}^2}\) and the volume of the water heater is \(\boxed{339292.01 \, \text{cm}^3}\).
