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Now a pile of rice is against the wall with a base circumference of 60 chi and an altitude of 12 chi. What is the volume?

Another pile is at an inner corner, with a base circumference of 30 chi and an altitude of 12 chi. What is the volume?

Another pile is at an outer corner, with a base circumference of 90 chi and an altitude of 12 chi. What is the volume?



Answer :

GinnyAnswer
Sure, let's go through each step-by-step solution for calculating the volume of each pile of rice.

### Pile of Rice Against the Wall
1. Given:
- Base circumference = 60 chi
- Altitude = 12 chi

2. Volume Calculation:
The formula to calculate the volume of a pile of rice is given by:
[tex]\[ V = \frac{C \times h^2}{4 \times \pi} \][/tex]
- Where [tex]\( V \)[/tex] is the volume
- [tex]\( C \)[/tex] is the base circumference
- [tex]\( h \)[/tex] is the altitude
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159

Plugging in the values, we get:
[tex]\[ V = \frac{60 \times 12^2}{4 \times \pi} \][/tex]
[tex]\[ V \approx 687.55 \text{ cubic chi} \][/tex]

### Pile of Rice at an Inner Corner
1. Given:
- Base circumference = 30 chi
- Altitude = 12 chi

2. Volume Calculation:
Using the same formula:
[tex]\[ V = \frac{C \times h^2}{4 \times \pi} \][/tex]

Plugging in the values:
[tex]\[ V = \frac{30 \times 12^2}{4 \times \pi} \][/tex]
[tex]\[ V \approx 343.77 \text{ cubic chi} \][/tex]

### Pile of Rice at an Outer Corner
1. Given:
- Base circumference = 90 chi
- Altitude = 12 chi

2. Volume Calculation:
Using the same formula:
[tex]\[ V = \frac{C \times h^2}{4 \times \pi} \][/tex]

Plugging in the values:
[tex]\[ V = \frac{90 \times 12^2}{4 \times \pi} \][/tex]
[tex]\[ V \approx 1031.32 \text{ cubic chi} \][/tex]

### Summary:
- The volume of the pile of rice against the wall is approximately [tex]\( 687.55 \)[/tex] cubic chi.
- The volume of the pile of rice at the inner corner is approximately [tex]\( 343.77 \)[/tex] cubic chi.
- The volume of the pile of rice at the outer corner is approximately [tex]\( 1031.32 \)[/tex] cubic chi.