Question

1. the formula for volume of a cylinder is ( v=pi r^{2} h ), where ( r ) is the radius of the circle and ( h ) is the height. determine the volume of this shape. use 3.14 for pi, ( pi ). volume units are in units ( ^{3} ) 7. the formula for volume of a cone is ( v=\frac{1}{3} pi r^{2} h ), where ( r ) is the radius of the circle and ( h ) is the height. determine the volume of this shape. use 3.14 for pi, ( pi ). volume units are in units ( ^{3} ) pythagorean section: draw in the right angle square, then determine the value of ( x ) for each triangle. #1 #2 ( a^{2}+b^{2}=c^{2} ) ( (x)^{2}+(6)^{2}=(10)^{2} ) #3 #4

Explanation:

Step1: Use Pythagorean theorem

Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\) (for right - angled triangles where \(c\) is the hypotenuse).

Step2: Solve for \(\#1\)

Given \(a = 14\), \(b=48\). Then \(x^{2}=14^{2}+48^{2}\).
\(x^{2}=196 + 2304\).
\(x^{2}=2500\).
\(x=\sqrt{2500}=50\).

Step3: Solve for \(\#2\)

Given \(b = 6\), \(c = 10\). Then \(x^{2}+6^{2}=10^{2}\).
\(x^{2}=100 - 36\).
\(x^{2}=64\).
\(x=\sqrt{64}=8\).

Step4: Solve for \(\#3\)

Assume it is a right - angled triangle (after drawing the right - angle square). Given \(a = 12\), \(b = 16\). Then \(x^{2}=12^{2}+16^{2}\).
\(x^{2}=144+256\).
\(x^{2}=400\).
\(x=\sqrt{400}=20\).

Step5: Solve for \(\#4\)

Assume it is a right - angled triangle (after drawing the right - angle square). Given \(b = 8\), \(c = 10\). Then \(x^{2}+8^{2}=10^{2}\).
\(x^{2}=100 - 64\).
\(x^{2}=36\).
\(x=\sqrt{36}=6\).

Answer:

\(\#1:50\); \(\#2:8\); \(\#3:20\); \(\#4:6\)