Question

Suppose you have a coffee mug with a circular cross-section and vertical sides (uniform radius). What is its inside radius if it holds 375 g of coffee when filled to a depth of 7.50 cm? Assume coffee has the same density as water.

a) 5.00 cm
b) 6.25 cm
c) 7.50 cm
d) 8.75 cm

Answer 1

Using the formula for the volume of a cylinder and the density of water, the inside radius of a coffee mug holding 375 g of coffee at a depth of 7.50 cm is calculated to be approximately 6.25 cm.

Step-by-step explanation:

To determine the inside radius of a coffee mug with a circular cross-section and vertical sides that holds 375 g of coffee at a depth of 7.50 cm, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height (or depth in this case).

Since the density of coffee is assumed to be the same as water, we can convert the mass of the coffee to volume using the density of water, which is 1 g/cm³. Hence, 375 g of coffee equates to 375 cm³ of coffee. We then have the equation 375 cm³ = πr²(7.50 cm).

Solving for r, we get:

r² = 375 cm³ / (π * 7.50 cm)

r = √(375 / (π * 7.50))

r ≈ 6.25 cm

Therefore, the inside radius of the coffee mug is approximately 6.25 cm, which corresponds to option (b).