Question

Find the radius of this ice cup. Round to the nearest tenth.

Answer 1

The inside radius of a coffee mug that holds 375 g of coffee at a depth of 7.50 cm can be calculated by rearranging the volume formula of a cylinder and solving for the radius, assuring that the density of coffee is the same as water.

Step-by-step explanation:

To find the inside radius of a coffee mug with a circular cross-section that holds 375 g of coffee filled to a depth of 7.50 cm, we first need to acknowledge that the density of coffee is equivalent to that of water, which is about 1 g/cm³ (1000 kg/m³). We can use the formula for the volume of a cylinder, V = πr²h, where V represents volume, r is the radius, and h is the height or depth of the liquid. Since 375 g of coffee is equivalent to 375 cm³ (because 1 g/cm³ = 1 cm³/g), we plug this value into our volume formula and solve for the radius.

To find the radius, you rearrange the volume equation to r = √(V/(πh)) and substitute in the volume (375 cm³) and the height (7.50 cm). The calculation will look like this: r = √(375 / (π * 7.50)). When you do the math and round to the nearest tenth, you get the radius of the coffee mug in centimeters.

Answer 2

The image forms a right triangle. The missing side is the radius of the ice cup.

Apply the Pythagorean theorem:

C^2 = a^2 + b^2

Where:

c= hypotenuse (the longest side ) = 4.5

a & b = the other 2 legs of the triangle (4 and x )

Replacing:

4.5^2 = 4^2 + x^2

Solve for x (the missing side)

20.25 = 16 + x^2

20.25-16 = x^2

4.25 = x^2

√4.25 = x

2.06 = x

x =2.1 in