The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?
1 answer:
Hey there :)
The volume formula of a cylinder is:
V =
r²h
The volume of the larger volume is given to be 9648³ and the height is 18 in
We need to find the radius first
9648 =r²(18)
= r²
536 =r²
= r²
= r
r ≈ 13.06
The ratio of the big cylinder to small cylinder is:
18 : 9 (given height)
So the big cylinder is 2 times bigger than the small cylinder
Therefore the radius of the big cylinder is as well 2 times bigger
r ≈ 6.53 ( the radius of the small radius )
V (of small cylinder) =(6.53)²(9)
= 1206 in³
The volume formula of a cylinder is:
V =
The volume of the larger volume is given to be 9648³ and the height is 18 in
We need to find the radius first
9648 =
536 =
r ≈ 13.06
The ratio of the big cylinder to small cylinder is:
18 : 9 (given height)
So the big cylinder is 2 times bigger than the small cylinder
Therefore the radius of the big cylinder is as well 2 times bigger
r ≈ 6.53 ( the radius of the small radius )
V (of small cylinder) =
= 1206 in³
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Answer:
The number of bacteria at initial = 187
Step-by-step explanation:
Given that the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t.
Integrating both side we get
㏑ N = k t + C ------- (1)
Now given that after 3 hours it is observed that 500 bacteria are present and after 10 hours 5000 bacteria are present.
⇒ ㏑ 500 = 3 k + C -------- (2)
⇒ ㏑ 5000 = 10 k + C ------ (3)
⇒ ㏑ 5000 - ㏑ 500 = 7 k
⇒ ㏑ = 7 k
⇒ ㏑ 10 = 7 k
⇒ k = 0.329
Put this value of k in equation (2),
⇒ ㏑ 500 = 3 × 0.329 + C
⇒ C = 5.23
Put this value of C in equation 1 we get,
⇒ ㏑ N = k t + 5.23
Initially when t = 0 , then
⇒ ㏑ N = 5.23
⇒ N = 187
Thus the number of bacteria at initial = 187