Question

See the picture below

Answer 1

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 = $\frac{\frac{4}{3}\pi r^3}{2}$

radius is given as 4, so,

Volume of Hemisphere = $\frac{\frac{4}{3}\pi r^3}{2}\\=\frac{\frac{4}{3}\pi (4)^3}{2}\\=134.04$

Now, Volume of Cone = $\frac{1}{3}\pi r^2 h$

Where radius is 4 and height is 10, so,

Volume of Cone = $\frac{1}{3}\pi r^2 h\\=\frac{1}{3}\pi (4)^2 (10)\\=167.55$

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 = $2\pi r^2\\=2\pi (4)^2\\=100.53$

Surface Area of Cone = $\pi r^2+\pi rl$

We dont need to use the first part, $\pi r^2$  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 = $\pi rl\\=\pi (4)(10.77)\\=135.34$

Surface area of ice cream cone = 100.53 + 135.34 = 235.87 square centimeters