Question

The total surface area of a hemisphere is 243pi. The volume of the hemisphere is K pi. Find the value of k

Answer 1

The value of k would be 486

Given

• total surface area of a hemisphere is 243pi.
• volume of the hemisphere is K pi

To find

• value of k

Solution

we are provided with the total surface area of the hemisphere as well and expression of the volume of the hemisphere and are asked to find the value of k contained in the expression of volume of the hemisphere.

the total surface area of the hemisphere would be,

half the surface area of the sphere + area of the circle

or, 2πr^2 + πr^2

or, 3πr^2

this area is given as 243 Pi

or, 3πr^2 = 243π

or, 3r^2 = 243

or, r^2 = 81

or, r = 9

(radius cannot be negative)

now the volume of the hemisphere would be,

2/3πr^3

or, 2/3 π 9^3

or, 6π 9^2

this is given as Kπ

or, Kπ = 6π 9^2

or, k = 6× 9^2

or, k = 486

Therefore, the value of k would be 486

Answer 2

Concept Introduction:-

A hemisphere has one curved floor and one flat face withinside the formed of the circle.

Given Information:-

We have been given that The total surface area of a hemisphere is $243$ pi. The volume of the hemisphere is $K$ pi.

To Find:-

We have to find that value of $K$.

Solution:-

According to the problem

the total surface area of the hemisphere would be,

half the surface area of the sphere $+$ area of the circle

$2\pi r^2 + \pi r^2\\3\pi r^2$

This area is given as $243$ Pi

$3\pi r^2 = 243\pi\\3r^2 = 243\\r^2 = 81\\r = 9$

now the volume of the hemisphere would be,

$2/3\pi r^3\\2/3 \pi 9^3\\6\pi 9^2$

this is given as $K\pi$

$K\pi = 6\pi 9^2\\k = 6\times 9^2\\k = 486$

Final Answer:-

The value of $K$ is $486$.

#SPJ2