Question

4.8 understand: the ultimate volume showdown!
show what you know
a cylindrical juice bottle has a radius of 6 cm and a height of 25 cm. using π≈3.14, what is the bottles approximate volume? choose the closest answer.
2500 cm³
3200 cm³
2400 cm³
2800 cm³

Explanation:

Step1: Write the formula for the volume of a cylinder

The formula for the volume \( V \) of a cylinder is \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values into the formula

Given \( r = 6\space cm\), \( h=25\space cm\), and \( \pi\approx3.14\).
Substitute these values: \( V = 3.14\times6^{2}\times25\).
First, calculate \( 6^{2}=36\).
Then, \( V=3.14\times36\times25\).
Since \( 36\times25=(40 - 4)\times25=40\times25-4\times25 = 1000 - 100=900\).
So, \( V=3.14\times900\).

Step3: Calculate the final value

\( V = 3.14\times900=2826\space cm^{3}\).

Answer:

\( 2800\space cm^{3}\) (since \( 2826\) is closest to \( 2800\) among the given options)