Question

find the volume of the solid. for formulas containing π, give the exact answer approximation using \\(\frac{22}{7}\\) for π. the exact value of the volume is 48π cubic yards. (simplify your answer. type an exact answer in terms of π.) the approximate value of the volume is \\(\square\\) (simplify your answer. type a whole number, fraction, or mixed number.)

Explanation:

Step1: Substitute π with 22/7

We know the exact volume is \( 48\pi \) cubic yards. To find the approximate value, we substitute \( \pi = \frac{22}{7} \) into the formula. So we have \( 48\times\frac{22}{7} \).

Step2: Calculate the product

First, multiply 48 and 22: \( 48\times22 = 1056 \). Then divide by 7: \( \frac{1056}{7}=\frac{1056\div7}{1} \approx 150.857 \)? Wait, no, wait, 4822 is 1056, and 1056 divided by 7: 7150 = 1050, 1056 - 1050 = 6, so it's \( 150\frac{6}{7} \)? Wait, no, wait, 4822/7: 4822 = 1056, 1056/7 = 150.857... But wait, maybe I made a mistake. Wait, 4822=1056, 1056 divided by 7: 7150=1050, 1056-1050=6, so 150 and 6/7? Wait, no, 4822/7: let's compute 48(22/7) = (4822)/7 = 1056/7 = 150.857... But the problem says to type a whole number, fraction, or mixed number. Wait, 1056 divided by 7: 7150 = 1050, remainder 6, so it's \( 150\frac{6}{7} \)? Wait, no, 4822=1056, 1056/7=150.857142..., but maybe I miscalculated. Wait, 4822: 4022=880, 822=176, 880+176=1056. Then 1056/7: 7150=1050, 1056-1050=6, so 150 6/7. But let's check again. Wait, the exact volume is 48π, so substituting π=22/7, we get 48(22/7) = (4822)/7 = 1056/7 = 150.857..., but as a fraction, it's 1056/7, which simplifies to 150 6/7. But maybe the problem expects a whole number? Wait, no, 4822/7: 48 and 22/7: 4822=1056, 1056/7=150.857, but maybe I made a mistake in the problem. Wait, maybe the solid is a cylinder? Wait, the exact volume is 48π, so if it's a cylinder, volume is πr²h=48π, so r²h=48. But regardless, the approximate value is 48(22/7). Let's compute that: 4822=1056, 1056/7=150.857..., but as a fraction, 1056/7=150 6/7. But maybe the problem wants an integer? Wait, no, 22/7 is an approximation, so 48(22/7)= (4822)/7=1056/7=150.857, but maybe the problem has a typo, or maybe I miscalculated. Wait, 4822=1056, 1056 divided by 7: 7150=1050, 1056-1050=6, so 150 6/7. But let's check with a calculator: 22 divided by 7 is approximately 3.142857. Then 483.142857≈483 + 480.142857≈144 + 6.857≈150.857, which is 150 6/7. So the approximate value is 150 6/7 or 1056/7. But the problem says "Type a whole number, fraction, or mixed number." So 1056/7 simplifies to 150 6/7. But maybe the problem expects 150.86, but no, it says fraction or mixed number. So 150 6/7. Wait, but let's check again. 48*22=1056, 1056/7=150.857142..., which is 150 and 6/7. So that's the approximate value.

Answer:

\( \frac{1056}{7} \) (or \( 150\frac{6}{7} \)) cubic yards.