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.

qwertyzz Sep 14, 2020

#1**0 **

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**

** =300pi**

**Sorry, I misread the question.**

Guest Sep 14, 2020

edited by
Guest
Sep 14, 2020

#3**+1 **

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-

Ab=πR2Ab=πR2

The total surface area of the hemisphere-

At=Ab+2πR2At=πR2+2πR2At=3πR2At=Ab+2πR2At=πR2+2πR2At=3πR2

Answer and Explanation:

Given that the area of the base of a hemisphere is 100π.100π.

So

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!?!?!?!?!?**

iGuest Sep 14, 2020