Question

please check the answer
The height is 50 cm and the radius is 22 cm.
Find the volume of the cylinder minus the hemisphere

Answer 1

A) 53,698.2 cc
B) 161,094.6 cc
C) 214,792.8 cc
D) 415,818.0 cc

Answer 2

I got A as my first answer, but when I did that I forgot to divide the volume of the hemisphere by 2
and I got A


when I didvided the volume of the hemisphere I got as the answer 64843 which is not included in the choices

Answer 3

what should I do ?

Answer 4

Hmm... What is the volume of the half hemisphere?

Answer 5

A sphere is a perfectly round geometrical object that is three dimensional, with every point on its surface equidistant from its center. Many commonly-used objects such as balls or globes are spheres. If you want to calculate the volume of a sphere, you just have to find its radius and plug it into a simple formula, V = ⁴⁄₃πr³

Answer 6

here is the calc if the rad is 1

Answer 7

I got this 2/3 pi r^3 = 2/3 * 3.14 * 22^3 = 22289.81
divide by 2 11144.90667

Answer 8

first you must cube the radius so 22*22*22

Answer 9

it is 10648

Answer 10

should I use given
formula instead ⁴⁄₃πr³

Answer 11

ok and then?

Answer 12

then you must multiply it by 3/4, or .75

Answer 13

what did you get?

Answer 14

7986

Answer 15

oops I meant 4/3

Answer 16

sorry on that

Answer 17

14197.333

Answer 18

ok now multiply that by PI, or 3.14, to get the volume.

Answer 19

that will be 44579.62667

Answer 20

but then you will have to divide it by 2

Answer 21

because its half the size.

Answer 22

so it will be 22289.81

Answer 23

yes

Answer 24

yes. now put that number aside, and find the entire cylindrer volume incliding the sphere

Answer 25

then minus what you get by the volume of the sphere half

Answer 26

and theres your answer

Answer 27

ok I used this to find the v. of cylinder pi r^2 h = 3.14 * 22^2 *50
I got 75988

Answer 28

did u minus the sphere half?

Answer 29

yes

Answer 30

Ok than that's the answer

Answer 31

by subtracting I got 53698.19

Answer 32

which is A

Answer 33

thanks a lot @Dbzfan836 for your help :)

Answer 34

Good!

Answer 35

Thnks for the medal

Answer 36

These problems are usually a bit easier if you keep \(\pi\) as a symbol for as long as possible, and other numbers as fractions instead of decimals.

Here the volume of the hemisphere is \[V_{hemi}=\frac\{1}{2}*\frac{4}{3}\pi(22)^3=\frac{21296}{3}\pi\]

Volume of the cylinder is \[V_{cyl}=\pi(22)^2(50)=24200\pi=\frac{72600}{3}\pi\]

Volume left after subtracting hemisphere is \[V_{rem}=V_{cyl}-V_{hemi}=\frac{72600-21296}{3}\pi\approx 53725\]the larger value is because the rounded \(\pi\) down to \(3.14\) for the calculation, and when you are multiplying by a number with 5 places to the left of the decimal point, the places to the right of the decimal point have an appreciable impact. One more argument for keeping work and answers in exact symbolic form; you can easily convert from that to a decimal if needed, but going in the opposite direction is more difficult to do, especially if you have done the intermediate calculations with lower precision. I did the entire calculation above mentally and got a closer answer than they did!