The area of the base of a hemisphere is 100pi. What is the total surface area of the hemisphere? Express your answer in terms of pi.
Base area of a hemisphere = pi x r^2, where r = radius.
pi x r^2 = 100pi divide both sides by pi
r^2 = 100 Take the square root of both sides
r = 10 - the radius of the hemisphere
Surface area of a hemisphere WITHOUT THE BASE =2 x pi x r^2
=2 x pi x 10^2 + Base area
= 200pi + 100pi
Sorry, I misread the question.
Before understanding the sphere we have to understand a sphere.
A sphere is a 3-dimensional geometry that is a round shape whose all points on the surface have a fixed distance from a point that is at a definite spot inside it.
This definite point inside the sphere is called the center and this fixed distance is called the radius of the sphere.
A hemisphere is half part of a sphere that is obtained when the sphere is divided into two identical parts by cutting it from the center.
The radius of the hemisphere will be the same as the sphere from which it is obtained.
The base of a hemisphere is a circle so the area of the base is computed as-
The total surface area of the hemisphere-
Answer and Explanation:
Given that the area of the base of a hemisphere is 100π.100π.
Ab=100ππR2=100πR2=100R=√100R=10 unitsAb=100ππR2=100πR2=100R=100R=10 units
We know that the total surface area of a hemisphere is-
At=3πR2At=3π(10)2At=3π(100)At=300π square unitsAt=3πR2At=3π(10)2At=3π(100)At=300π square units
So the total surface area of the hemisphere is 300π square units.
... Now WHERE IS MY COOKIE!?!?!?!?!?