Answer:
1. The curved surface area of the cone is 282.74 cm²
2. Radius of sphere r = 4.924 m
Step-by-step explanation:
1. Height of cone = 12 cm
Diameter of base of cone = 10 cm
Surface Area of cone = ?
The formula used is: [tex]A=\pi r(r+\sqrt{h^2+r^2})\\[/tex]
h= 12 cm
r = diameter/2 r = 10/2 = 5 cm
Putting values and finding surface area
[tex]A=\pi r(r+\sqrt{h^2+r^2})\\A=3.14*5 (5+\sqrt{(12)^2+(5)^2})\\A=15.7 (5+\sqrt{144+25})\\A=15.7 (5+\sqrt{169})\\A=15.7 (5+13)\\A=15.7(18)\\A=282.74 \ cm^2[/tex]
So, the curved surface area of the cone is 282.74 cm²
2. Sphere of Volume = 500 m³
We need to find radius of sphere
The formula used is: [tex]Volume=\frac{4}{3}\pi r^3[/tex]
Putting values and finding radius of sphere
[tex]Volume=\frac{4}{3}\pi r^3\\500=\frac{4}{3}*3.14* r^3\\500=4.186*r^3\\=> r^3=\frac{500}{4.186}\\r^3=119.446\\Taking \ cube \ root \ on \ both \ sides.\\\sqrt[3]{r^3}=\sqrt[3]{119.446}\\r= 4.924 \ m\\[/tex]
So, Radius of sphere r = 4.924 m
