Question

what is the volume of this sphere? use π ≈ 3.14 and round your answer to the nearest hundredth. 87 m cubic meters submit

Explanation:

Step1: Recall the formula for the volume of a sphere.

The formula for the volume \( V \) of a sphere is \( V=\frac{4}{3}\pi r^{3} \), where \( r \) is the radius of the sphere. From the diagram, the radius \( r = 87\space m \).

Step2: Substitute the values into the formula.

Substitute \( \pi\approx3.14 \) and \( r = 87 \) into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\times3.14\times(87)^{3}\\ &=\frac{4}{3}\times3.14\times658503\\ \end{align*}$$

\]

Step3: Calculate the value.

First, calculate \( \frac{4}{3}\times3.14=\frac{12.56}{3}\approx4.1867 \)
Then, multiply by \( 658503 \):
\( 4.1867\times658503\approx4.1867\times658503 \)
\( 4.1867\times658503 = 4.1867\times(600000 + 58503)=4.1867\times600000+4.1867\times58503 \)
\( 4.1867\times600000 = 2512020 \)
\( 4.1867\times58503\approx4.1867\times58500 = 4.1867\times50000+4.1867\times8500=209335+35586.95 = 244921.95 \)
Adding these two results: \( 2512020+244921.95 = 2756941.95 \) (approximate, more accurately we can calculate directly: \( \frac{4}{3}\times3.14\times87^{3}=\frac{4\times3.14\times658503}{3}=\frac{8270779.56}{3}=2756926.52 \))

Wait, let's do the calculation more accurately:

\( 87^{3}=87\times87\times87 = 7569\times87 = 658503 \)

\( \frac{4}{3}\times3.14\times658503=\frac{4\times3.14\times658503}{3} \)

\( 4\times3.14 = 12.56 \)

\( 12.56\times658503 = 12.56\times600000+12.56\times58503=7536000+734797.68 = 8270797.68 \)

Then divide by 3: \( \frac{8270797.68}{3}=2756932.56 \)

Answer:

\( 2756932.56 \)