1)
The formula for calculating the cone volume is:
\(V = \frac{ \pi *r^2*h}{3}\)
Data:
V (volume) = ?
h (height) → h = 12 in
d (diagonal) = 9 in , if: d = 2r , soon: 9 = 2r → 2r = 9 → r = 9/2 → r = 4.5 in
Use: \(\pi \approx 3.14\)
Solving:
\(V = \frac{ \pi *r^2*h}{3}\)
\(V = \frac{ 3.14 *4.5^2*12}{3}\)
\(V = \frac{ 3.14 *20.25*12}{3}\)
\(V = \frac{763.02}{3}\)
\(\boxed{\boxed{V = 254.34\:in^3}}\end{array}}\qquad\quad\checkmark\)
2)
The circle area formula is: \(A = \pi * r^2\)
Data:
A (area) = ?
d (diagonal) = 19 Km , if: d = 2r , soon: 19 = 2r → 2r = 19 → r = 19/2 → r = 9.5 Km
Use: \(\pi \approx 3.14\)
Solving:
\(A = \pi * r^2\)
\(A = 3.14*9.5^2\)
\(A = 3.14*90.25\)
\(\boxed{\boxed{A = 283.385\:Km^2}}\end{array}}\qquad\quad\checkmark\)
3) False, because it's the volume, the number of cubic units needed to fill a space.
