Question

1. a water tank has been purchased for the farm. it will be used to provide water for the cattle. it is a cylindrical tank that is 2.6 feet tall. the area of the bottom of the tank is 9.3 square feet. if the cattle drink 204 cubic feet of water a day, how many times per day will the tank have to be filled?

Explanation:

Step1: Calculate volume of cylindrical tank

The volume \( V \) of a cylinder is given by \( V = \text{base area} \times \text{height} \). Here, base area is \( 9.3 \) square feet and height is \( 2.6 \) feet. So, \( V = 9.3 \times 2.6 \).
\( 9.3\times2.6 = 24.18 \) cubic feet.

Step2: Find number of times to fill

To find how many times the tank needs to be filled, divide the total water drunk per day by the volume of the tank. Let \( n \) be the number of times. So, \( n=\frac{204}{24.18} \).
\( \frac{204}{24.18}\approx 8.44 \). Since we can't fill a fraction of a time less than 1 fully, we need to round up (but in practical terms, the calculation gives approximately 8.44, so we can say about 9 times? Wait, no, wait: 24.18*8=193.44, 24.18*9=217.62. Wait, 204 - 193.44 = 10.56, which is more than 24.18? No, wait, 24.18*8=193.44, 204-193.44=10.56, which is less than 24.18? Wait no, 24.18 is the volume. Wait, 204 divided by 24.18: let's calculate 204 ÷ 24.18. Let's do this division: 24.18*8=193.44, 204-193.44=10.56. 10.56/24.18≈0.436. So total is 8.436, so we need to fill it 9 times? Wait, no, the question is how many times per day will the tank have to be filled. So if the tank holds 24.18 cubic feet, and they drink 204, then 204/24.18 ≈8.44. So we need to fill it about 9 times? Wait, no, maybe I made a mistake. Wait, 9.3*2.6: 9*2.6=23.4, 0.3*2.6=0.78, so 23.4+0.78=24.18. Correct. Then 204/24.18: let's compute 204 ÷24.18. Let's multiply numerator and denominator by 100 to eliminate decimals: 20400 ÷2418. Divide numerator and denominator by 6: 3400 ÷403 ≈8.436. So approximately 8.44 times. But since you can't fill a fraction of a time, you have to fill it 9 times? Wait, no, the problem is probably expecting a decimal or maybe we can round to the nearest whole number. Wait, maybe the question allows decimal or we can just compute the exact value. Wait, maybe I miscalculated. Wait 24.18*8=193.44, 204-193.44=10.56. 10.56 is less than 24.18, so 8 times would not be enough, because 8 times only provides 193.44, which is less than 204. So we need to fill it 9 times. Wait, but maybe the problem expects the decimal. Wait, let's check again.

Wait, the formula for the volume of a cylinder is \( V = A \times h \), where \( A \) is the base area and \( h \) is the height. So that's correct. Then dividing total water by volume gives the number of times. So 204 /24.18 ≈8.44. So the answer is approximately 9 times? Wait, no, maybe the question is okay with a decimal. Wait, let's see: 24.18*8=193.44, 204-193.44=10.56. So 10.56 cubic feet more is needed, so we need to fill it a 9th time. So the answer is 9? Wait, but maybe the problem expects the exact division. Wait, let's do 204 ÷24.18:

24.18 × 8 = 193.44

204 - 193.44 = 10.56

10.56 /24.18 = 0.436

So total is 8.436, so approximately 8.44 times. But in real life, you can't fill a fraction, so you have to fill it 9 times. But maybe the problem just wants the decimal. Let's check the calculation again.

Wait, 9.3*2.6: 9*2=18, 9*0.6=5.4, 0.3*2=0.6, 0.3*0.6=0.18. So (9*2)+(9*0.6)+(0.3*2)+(0.3*0.6)=18+5.4+0.6+0.18=24.18. Correct.

204 divided by 24.18: let's use a calculator approach. 24.18*8=193.44, 204-193.44=10.56. 10.56/24.18=0.436. So 8.436, which is approximately 8.44. So the answer is approximately 9 times? Wait, no, maybe the problem expects the answer as 9? Wait, maybe I made a mistake in the volume. Wait, no, the base area is 9.3 square feet, height 2.6 feet, so volume is 9.3*2.6=24.18. Correct. Then 204/24.18≈8.44. So the tank has to be filled about 9 times per day (since 8 times would not provide enough water).

Answer:

\boxed{9} (or approximately 8.44, but since we can't fill a fraction, we round up to 9)