Question

The volume of a tree stump can be modeled by considering it as a right cylinder. Lauren measures its height as 0.8 ft and its volume as 26146 cubic inches. Find the stump’s diameter in inches. Round your answer to the nearest tenth if necessary. HELP ASPPPP

Answer 1

• 58.9 in

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Volume of a cylinder:

• V = πr²h or
• V = π(d²/4)h, where r - radius, d - diameter, h - height

We are given that:

• h = 0.8 ft and
• V = 26146 in³

Convert the height into inches (1 ft = 12 in) and find the diameter:

• 26146 = 3.14*(d²/4)*(0.8*12)
• 26146 = 7.536d²
• d² = 26146/7.536
• d² = 3469.4798
• d = √3469.4798
• d = 58.9 (rounded)

Answer 2

59 inch

Explanation:

• Given the volume formula for a right cylinder:

Volume = π × r² × height

• Convert the height from feet to inches:

0.8 ft × 12 inches/foot = 9.6 inches

• Plug in the values:

26146 = π × r² × 9.6

• Divide both sides of the equation by 9.6π:

r² = 26146 / (9.6π)

• To find the radius, take the square root of both sides:

r = √(26146 / (9.6π))

r ≈ √(26146 / (9.6 * 3.14159))

• Calculate the value inside the square root:

r ≈ √(26146 / 30.16963144)

• Now, find the square root of the division:

r ≈ √867.8825

• Evaluate the square root:

r ≈ 29.478

Hence, the radius of the stump is approximately 29.478 inches.

• To find the diameter, double the radius:

diameter ≈ 2 × 29.478 ≈ 58.956 inches.

Rounding to the nearest tenth, the stump's diameter is approximately 59.0 inches.