The diameter of one side of a 10-foot log is approximately 13 inches. The diameter of the other side of the log is approximately 11 inches. Which is the best way to estimate the volume in cubic feet of the log?
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Answer with explanation:
As, the log is in the shape of Frustum.We will use the Formula of frustum to find the volume.
A=13 inches,B=11 inches, H=10 feet
Volume of Frustum
[tex]=\frac{\pi\times H}{3}[A^2+B^2+AB]\\\\=\frac{3.14 \times 10}{3}\times[(\frac{13}{2})^2+(\frac{11}{2})^2+\frac{13}{2} \times \frac{11}{2}]\\\\=\frac{31.4}{3} \times [\frac{169}{4}+\frac{121}{4}+\frac{143}{4}]\\\\=\frac{31.4}{3} \times \frac{433}{4}\\\\=1133[/tex]
Ok, when you will round up the numbers, in equation of Volume it will give
Volume of frustum = 3 × 36 × 10 cubic feet(Approximate)
Because ,
[tex]\rightarrow\frac{3.14 \times 10}{3}=10\\\\\rightarrow \frac{169}{4}+\frac{121}{4}+\frac{143}{4}=36 \times 10[/tex]
Option C: