We have been given that an artist cuts the bottom 4 inches from an empty sphere with a radius of 12 inches to make a bowl. We are asked to find the length of the rim of the bowl.

The rim of the bowl will be equal to the perimeter of circle with radius of 12 inches.

$\text{Perimeter of circle}=2\pi r$ , where r represents radius of circle.

$\text{Perimeter of circle}=2\pi (12\text{ inches})$

$\text{Perimeter of circle}=24\pi \text{ inches}$

$\text{Perimeter of circle}=75.39822 \text{ inches}$

$\text{Perimeter of circle}\approx 75.4 \text{ inches}$

Therefore, the rim of the bowl is approximately 75.4 inches.

6 0

2 years ago

A rectangle has an area of 20 ft.² in a similar rectangle has an area of 180 ft.² what is the ratio of areas of the similar

vovikov84 [41]

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{cccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------\\\\$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s^2}{s^2}=\cfrac{20}{180}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{20}{180}\implies \cfrac{s}{s}=\sqrt{\cfrac{20}{180}}
\\\\\\
\cfrac{s}{s}=\cfrac{\sqrt{20}}{\sqrt{180}}\implies \cfrac{s}{s}=\cfrac{2\sqrt{5}}{6\sqrt{5}}\implies \cfrac{s}{s}=\cfrac{2}{6}\implies \cfrac{s}{s}=\cfrac{1}{3}$

6 0

3 years ago