Calculate the surface area of each of the following spheres and hemispheres. (Use π = 3.142)

* Sphere with radius 18cm
* Hemisphere with diameter 60cm

Question

High School

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Answer :

LiamAlexanderSmith LiamAlexanderSmith · Answer 1 · 2024-04-06T22:45:15-04:00

To calculate the surface area of a sphere and a hemisphere, we will apply the respective formulas. Let's break down each part of the problem:

Sphere with radius 18 cm:
The formula for the surface area of a sphere is given by:
[tex]A = 4\pi r^2[/tex]
Where [tex]A[/tex] is the surface area and [tex]r[/tex] is the radius of the sphere.
Substituting the given radius [tex]r = 18 \text{ cm}[/tex] and [tex]\pi = 3.142[/tex]:
[tex]A = 4 \times 3.142 \times (18)^2[/tex]
[tex]A = 4 \times 3.142 \times 324[/tex]
[tex]A = 4069.632 \text{ cm}^2[/tex]
Therefore, the surface area of the sphere is [tex]4069.632 \text{ cm}^2[/tex].
Hemisphere with diameter 60 cm:
First, find the radius of the hemisphere. Since the diameter is [tex]60 \text{ cm}[/tex], the radius [tex]r[/tex] is:
[tex]r = \frac{60}{2} = 30 \text{ cm}[/tex]
The surface area of a hemisphere (including its base) is given by:
[tex]A = 3\pi r^2[/tex]
Substituting [tex]r = 30 \text{ cm}[/tex] and [tex]\pi = 3.142[/tex]:
[tex]A = 3 \times 3.142 \times (30)^2[/tex]
[tex]A = 3 \times 3.142 \times 900[/tex]
[tex]A = 8483.4 \text{ cm}^2[/tex]
Therefore, the surface area of the hemisphere, including its base, is [tex]8483.4 \text{ cm}^2[/tex].