The density of water is 1 gram per cm^3 An object floats in water if its density is less than water's density, and it sinks if its density is greater than water's. Suppose a lime with mass 90 grams is in the shape of a sphere with radius 2.5 centimeters. Will the lime sink or float in water? Explain or show your reasoning.

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The density of water is 1 gram per cm^3 An object floats in water if its density is less than water's density, and it sinks if its density is greater than water's. Suppose a lime with mass 90 grams is in the shape of a sphere with radius 2.5 centimeters. Will the lime sink or float in water? Explain or show your reasoning.

Answer 1

The lime will sink. *Here's why: ## Step 1 Calculating the volume of the sphere using \( V = \frac{4}{3}\pi r^3 \), where \( r \) is the radius (2.5 cm). ## Step 2 Calculating the density using \( \rho = \frac{m}{V} \), where \( m \) is mass (90 grams) and \( V \) is volume. ## Step 3 The density of lime is calculated to be approximately 1.38 g/cm^3. ## Step 4 Since the density of lime is slightly higher than that of water (1.38 g/cm^3 > 1 g/cm^3), the lime will sink in the water.

Answer 2

## Step 1 The volume of the lime can be calculated using the formula for the volume of a sphere, which is given by ### \( V = \frac{4}{3}\pi r^3 \) where \( r \) is the radius of the sphere. The radius of the lime is given as 2.5 cm. ## Step 2 Next, we calculate the density of the lime using the formula for density, which is ### \( \rho = \frac{m}{V} \) where \( m \) is the mass of the object and \( V \) is its volume. The mass of the lime is given as 90 grams and the volume is calculated in the previous step. ## Step 3 Finally, we compare the density of the lime with the density of water. If the density of the lime is less than or equal to the density of water, the lime will float. If the density of the lime is greater than the density of water, the lime will sink.

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