Answer:
a) 301.59 cubic centimeters
b) 235.87 square centimeters
Step-by-step explanation:
a)
Volume of ice cream cone is volume of hemisphere PLUS volume of cone.
Volume of Hemisphere = [tex]\frac{\frac{4}{3}\pi r^3}{2}[/tex]
radius is given as 4, so,
Volume of Hemisphere = [tex]\frac{\frac{4}{3}\pi r^3}{2}\\=\frac{\frac{4}{3}\pi (4)^3}{2}\\=134.04[/tex]
Now, Volume of Cone = [tex]\frac{1}{3}\pi r^2 h[/tex]
Where radius is 4 and height is 10, so,
Volume of Cone = [tex]\frac{1}{3}\pi r^2 h\\=\frac{1}{3}\pi (4)^2 (10)\\=167.55[/tex]
Volume of Ice Cream Cone = 134.04 + 167.55 = 301.59 cubic centimeters
b)
Surface area of ice cream cone is surface area of hemisphere PLUS surface area of cone.
Surface Area of Hemisphere = [tex]2\pi r^2\\=2\pi (4)^2\\=100.53[/tex]
Surface Area of Cone = [tex]\pi r^2+\pi rl[/tex]
We dont need to use the first part, [tex]\pi r^2[/tex] since it is "inside". We need to find l, slant height, by using pythagorean theorem on a triangle we can make (bottom right).
4^2 + 10^ 2 = l^2
16 + 100 = l^2
116 = l^2
l = 10.77
Now to find the surface area of cone = [tex]\pi rl\\=\pi (4)(10.77)\\=135.34[/tex]
Surface area of ice cream cone = 100.53 + 135.34 = 235.87 square centimeters
