A solid metal cylinder with height of 10 inches and radius of 6 cm has a cylinder-shaped hole drilled through it. The cylinder shaped hole has a radius of 2 cm.
What is the volume of the remaining cylinder with the hole
Answers
Step-by-step explanation:
The volume element in cylindrical coordinates:
dV = r dθ dr dz
0 ≤ θ < 2π, r0 ≤ r ≤
√
R2 − z
2
, −h ≤ z ≤ +h,
where R is the radius of the original sphere (a quantity we do not know). The quantity r0
is the radius of the bored out cylinder:
r0 =
√
R2 − h
2
. (1)
Integrating over the upper-half of the solid and multiplying by two:
V = 2 Z h
z=0
Z √
R2−z
2
r=r0
Z 2π
0
dV
= 2 Z h
z=0
Z √
R2−z
2
r=r0
Z 2π
0
r dθ dr dz
= 2πh
R
2 −
h
2
3
− r
2
0
.
By putting in r0 from (1) we get
V =
4
3
πh3
.
Answer:
In given figure wooden right circular cylinder radius 2 m and height 6 m
In cylinder hole of diameter 2 m drilled though center
Then total surface area of resulting figure = area outer curved surface + area of two circular ends + area outer curved surface − area of two circular end of hole = 2π×2×6+2π(2)2+2π×1×6−2π×(1)2
=24π+8π+12π−2π
=42π