Solve the problem.
-The height of a vase is 5 inches. The table shows the circumference of the vase (in inches) at half-inch intervals starting from the top down. Estimate the volume of the vase by using the Trapezoidal rule with $n = 10$. Round your answer to the nearest thousandth. [Hint: you will first need to find the areas of the cross-sections that correspond to the given circumferences.]
$\begin{array}{lr}
{\text { Circumferences }} \
\hline 4.7 & 8.1 \
4.2 & 9.4 \
4.1 & 10.1 \
4.8 & 8.5 \
5.6 & 6.4 \
6.8 &
\end{array}$

A) $61.856 \mathrm { in } ^ { 3 }$
B) $62.876 \mathrm { in } ^ { 3 }$
C) $101.552$ in. 3
D) $105.479$ in. $^ { 3 }$

Question

Solve the problem.
-The height of a vase is 5 inches. The table shows the circumference of the vase (in inches) at half-inch intervals starting from the top down. Estimate the volume of the vase by using the Trapezoidal rule with $n = 10$. Round your answer to the nearest thousandth. [Hint: you will first need to find the areas of the cross-sections that correspond to the given circumferences.]
$\begin{array}{lr}
{\text { Circumferences }} \
\hline 4.7 & 8.1 \
4.2 & 9.4 \
4.1 & 10.1 \
4.8 & 8.5 \
5.6 & 6.4 \
6.8 &
\end{array}$

A) $61.856 \mathrm { in } ^ { 3 }$
B) $62.876 \mathrm { in } ^ { 3 }$
C) $101.552$ in. 3
D) $105.479$ in. $^ { 3 }$

Quizplus · Accepted Answer

To estimate the volume using the Trapezoidal rule, first calculate the area of each cross-section using the formula for the area of a circle $A = \frac{C^2}{4\pi}$, where $C$ is the circumference. Then apply the Trapezoidal rule to these areas over the height of the vase. The correct calculation results in approximately $61.856 \mathrm { in } ^ { 3 }$.

Solve the Problem n=10n = 10n=10 Round Your Answer to the Nearest Thousandth

Solve the Problem $n = 10$ Round Your Answer to the Nearest Thousandth