A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.
The volume of a rectangular prism is given by area of base × height The rate at which the tank is being filled is 1 liter per minute which we need to convert 1 liter = 1 dm³ But 1 dm = 10 cm. Hence 1 liter = (10 cm)³ = 1000 cm³ The height h of the water is related to the volume by volume = area of base × h In one minute the volume increases by 1 liter or 1000 cm³ and the height increases by h = volume / area of base = 1000 cm³ / 100 cm² = 10 cm
