Question

A company manufactures spherical containers for small toys, each with a radius of 2 cm. The company also sells a smaller product that is exactly half the shape of the original container. The resulting shape is a hemisphere. What is the surface area of the hemisphere? What is the surface area of the rounded part of the hemisphere? π in.2 What is the area of the circular base of the hemisphere? π in.2 What is the total surface area of the hemisphere? π in.2 Another student completed the same problem, but used the formula 3πr2 to determine the surface area. How would this solution compare to the surface area determined above? The solution would be the surface area determined above.

Answer 1

Answer:

$(a)8\pi cm^2\\(b)4\pi cm^2\\(c)12\pi cm^2\\(d)12\pi cm^2$

Step-by-step explanation:

Radius of the Sphere =2cm

(a)Surface Area of the rounded part of the Hemisphere

$=2\pi r^2\\=2\pi *2^2\\=8\pi cm^2$

(b)Area of the circular base of the hemisphere

$=\pi r^2\\=\pi *2^2\\=4\pi cm^2$

(c)Total Surface Area =Area of the rounded part+Area of the circular base

$=8\pi + 4\pi=12\pi cm^2$

(d)If another student completed the same problem using the formula,

Surface Area of a Hemisphere

$=3\pi r^2\\=3\pi *2^2\\=12\pi cm^2$

The solution would be the same as the surface area determined above.