To find the diameter of the needle, we need to use the formula for the volume flow rate, which is Q = v*A, where Q is the volume flow rate, v is the velocity of the air, and A is the cross-sectional area of the needle.

We know that Q = 103 cm^3/s and v = 6 cm/s. We can rearrange the formula to solve for A: A = Q/v = 103 cm^3/s / 6 cm/s = 17.17 cm^2.

The cross-sectional area of a circle (which is the shape of the needle's opening) is given by the formula A = π*(d/2)^2, where d is the diameter of the circle. We can rearrange this formula to solve for d: d = 2*sqrt(A/π).

Substituting A = 17.17 cm^2 into this formula gives d = 2*sqrt(17.17 cm^2 / π) = 4.67 cm.

However, the options are given in inches, so we need to convert from cm to inches. There are approximately 2.54 cm in an inch, so d = 4.67 cm / 2.54 = 1.84 inches.

The closest option to this is 1.8 inches, so that is the most likely answer.

Question

To find the diameter of the needle, we need to use the formula for the volume flow rate, which is Q = v*A, where Q is the volume flow rate, v is the velocity of the air, and A is the cross-sectional area of the needle.

We know that Q = 103 cm^3/s and v = 6 cm/s. We can rearrange the formula to solve for A: A = Q/v = 103 cm^3/s / 6 cm/s = 17.17 cm^2.

The cross-sectional area of a circle (which is the shape of the needle's opening) is given by the formula A = π*(d/2)^2, where d is the diameter of the circle. We can rearrange this formula to solve for d: d = 2*sqrt(A/π).

Substituting A = 17.17 cm^2 into this formula gives d = 2*sqrt(17.17 cm^2 / π) = 4.67 cm.

However, the options are given in inches, so we need to convert from cm to inches. There are approximately 2.54 cm in an inch, so d = 4.67 cm / 2.54 = 1.84 inches.

The closest option to this is 1.8 inches, so that is the most likely answer.

Knowee AI · Accepted Answer

To find the diameter of the needle, we need to use the formula for the volume flow rate, which is Q = v*A, where Q is the volume flow rate, v is the velocity of the air, and A is the cross-sectional area of the needle.

We know that Q = 103 cm^3/s and v = 6 cm/s. We can rearrange the formula to solve for A: A = Q/v = 103 cm^3/s / 6 cm/s = 17.17 cm^2.

The cross-sectional area of a circle (which is the shape of the needle's opening) is given by the formula A = π*(d/2)^2, where d is the diameter of the circle. We can rearrange this formula to solve for d: d = 2*sqrt(A/π).

Substituting A = 17.17 cm^2 into this formula gives d = 2*sqrt(17.17 cm^2 / π) = 4.67 cm.

However, the options are given in inches, so we need to convert from cm to inches. There are approximately 2.54 cm in an inch, so d = 4.67 cm / 2.54 = 1.84 inches.

The closest option to this is 1.8 inches, so that is the most likely answer.

You need to fill a basketball with air to play with it. You know that your pump expels air at a velocity of 6 cm/s. You know that the volume flow rate of air being pumped into the basketball is 103 cm^3/s. What is the diameter of your needle? 1 point1.8 inches5.5 inches2.4 inches1.1 inches

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