SOLUTION: A hemisphere of diameter 10cm is attached to a cylinder of equal diameter. If the total length of the shape is 20cm calculate: A) the surface area of the hemisphere B)length of

Algebra ->  Surface-area -> SOLUTION: A hemisphere of diameter 10cm is attached to a cylinder of equal diameter. If the total length of the shape is 20cm calculate: A) the surface area of the hemisphere B)length of       Log On


   

Question 1139006: A hemisphere of diameter 10cm is attached to a cylinder of equal diameter. If the total length of the shape is 20cm calculate:
A) the surface area of the hemisphere
B)length of cylinder
C) surface area of the whole shape
Found 3 solutions by greenestamps, MathLover1, Alan3354:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


diameter 10 --> radius 5

total length = length of cylinder + radius of hemisphere = 20 --> length of cylinder is 15

A) For a sphere, surface area is 4%28pi%29r%5E2
half of that for the hemisphere

B) see above

C) Lateral surface area of cylinder is 2%28pi%29rh
Area of bottom of cylinder (circle) is%28pi%29r%5E2

Fill in the measurements and do the calculations....

Leave answers in terms of pi unless directed otherwise.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A hemisphere of diameter 10cm is attached to a cylinder of equal diameter. If the total length of the shape is 20cm+calculate:

A) the surface area of the hemisphere
given: diameter d=10cm=> radius r=5cm
SA=2pi%2Ar%5E2
SA=2pi%2A%285cm%29%5E2
SA=2pi%2A25cm%5E2
SA=50pi%2Acm%5E2=> exact solution
+SA=157.14cm%5E2=>approximate solution

B) length of cylinder
If the total length of the shape is 20cm calculate, the length of cylinder will be difference between the total length of the shape and radius of cylinder
20cm-r=20cm-5cm=15cm

C) surface area of the whole shape
will be of the hemisphere plus surface area of cylinder (without one base)

surface area of cylinder is:
lateral surface area of cylinder is 2pi%2Arh
area of bottom of cylinder (circle) is r%5E2%2Api
SA%5Bc%5D=2rpi%2Ah%2Br%5E2%2Api....plug in r=5cm, h=15cm
SA%5Bc%5D=2%2A5cmpi%2A15cm%2B%285cm%29%5E2%2Api
SA%5Bc%5D=150pi%2Acm%5E2%2B25cm%5E2%2Api
SA%5Bc%5D=175pi%2Acm%5E2=> exact solution
SA%5Bc%5D=549.5cm%5E2=>approximate solution
=>surface area of the whole shape is:
total=50pi%2Acm%5E2%2B175pi%2Acm%5E2=225pi%2Acm%5E2=> exact solution
total=157.14cm%5E2%2B549.5cm%5E2=706.64cm%5E2=>approximate solution


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
There are some things you have to know:
-------
SA of a sphere = 4pi*r^2
SA of a cylinder = pi*r^2*h ---- the lateral area.
=========
Also:
Volume of a sphere = 4*pi*r^3/3
Volume of a cylinder = pi*r^2*h
---
You might notice that for a sphere, the SA is the 1st derivative of the volume
wrt to r.
--------
There are others, but you HAVE TO know these.
Like it or not.