Question

find the volume of the oblique cylinder below. round your answer to the nearest tenth if necessary.
answer attempt 1 out of 2
units³ submit answer

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder (including oblique cylinders) is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height (the perpendicular height, not the slant height).
From the diagram, the radius \( r = 5 \) and the perpendicular height \( h = 6 \).

Step2: Substitute the values into the formula

Substitute \( r = 5 \) and \( h = 6 \) into the formula:

$$ V = \pi \times (5)^2 \times 6 $$

First, calculate \( 5^2 = 25 \). Then, multiply by 6: \( 25 \times 6 = 150 \). So the volume is \( V = 150\pi \).

Step3: Calculate the numerical value

Using \( \pi \approx 3.14159 \), we have:

$$ V \approx 150 \times 3.14159 = 471.2385 $$

Rounding to the nearest tenth, we get \( 471.2 \) (wait, actually, \( 150\pi \approx 471.2 \) when rounded to the nearest tenth? Wait, no: \( 150\times3.1416 = 471.24 \), so to the nearest tenth is \( 471.2 \)? Wait, no, 471.24 rounded to the nearest tenth is 471.2? Wait, no, the tenths place is the first decimal, so 471.24: the digit in the hundredths place is 4, which is less than 5, so we round down, so 471.2? Wait, but actually, \( 150\pi \approx 471.2389 \), so to the nearest tenth is 471.2? Wait, no, 471.2389: the tenths digit is 2, the hundredths digit is 3, which is less than 5, so we keep the tenths digit as 2, so 471.2. Wait, but maybe I made a mistake in the height? Wait, the diagram shows the perpendicular height is 6, radius 5. So the formula is correct for oblique cylinders: the volume is the same as a right cylinder with the same base and perpendicular height. So \( V = \pi r^2 h = \pi \times 25 \times 6 = 150\pi \approx 471.2 \). Wait, but let me check again. Wait, 1503.1416 is 471.24, which to the nearest tenth is 471.2? Wait, no, 471.24: the tenths place is 2, the hundredths is 4, so we round down, so 471.2. Alternatively, maybe the height is 10? Wait, no, the slant height is 10, but the perpendicular height is 6. So the formula uses the perpendicular height, not the slant height. So that's correct. So the volume is \( 150\pi \approx 471.2 \) (or 471.2 when rounded to the nearest tenth). Wait, but actually, 1503.1415926535 = 471.238898, so to the nearest tenth is 471.2? Wait, no, 471.238898: the tenths digit is 2, the hundredths digit is 3, which is less than 5, so we round to 471.2. Wait, but maybe the problem expects using 3.14 for pi? Let's try that. 150*3.14 = 471.0, which is 471.0, but that's different. Wait, the problem says "round your answer to the nearest tenth if necessary". So using a more accurate pi, 150pi is approximately 471.2. So the volume is approximately 471.2 cubic units.

Answer:

\( 471.2 \) (or if using \( \pi = 3.14 \), \( 150 \times 3.14 = 471.0 \), but with more accurate pi, it's 471.2)