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lina2011 [118]
3 years ago
10

A solid is formed by adjoining two hemispheres to the ends of a circular cylinder. the radius of the hemispheres is the same as

the radius of the cylinder. the total volume of the solid is 16 cubic inches. what radius should the cylinder be to produce the minimum surface area?
Mathematics
1 answer:
nasty-shy [4]3 years ago
5 0
Total volume = Volume of Sphere + Volume of Cylinder
16 = (4/3)πr³ + πr²h
Express h in terms of r:
πr²h = 16 - (4/3)πr³
h = 16/πr² - (4/3)r

Next, let's solve for surface area:

Total Surface Area = SA of sphere + SA of cylinder
A = 4πr² + 2πrh
Substitute the expression for h:
A = 4πr² + 2πr[16/πr² - (4/3)r]
A = 4πr² + 32/r - (8/3)πr²

Find the derivative of A with respect to r and equate to zero.

dA/dr = 8πr - 32r⁻² - (16/3)πr = 0
Solve for r:
[(8/3)πr - 32/r² = 0]*r²
(8/3)πr³ - 32 = 0
r³ = 32*3/8π = 12/π
r = ∛(12/π)
<em>r = 1.56 inches</em>
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allsm [11]

Answer:

22

Step-by-step explanation:

5+12-2+7

17-2+7

15+7

22

6 0
3 years ago
. Ramu took a loan of 50000 rupees from a bank which charges 10% interest, compounded an- nually. He repaid 10000 rupees after o
Setler79 [48]

Answer:

= 30,550 rupee owed

Step-by-step explanation:

yr1 = 50000 x 0.10^1 = 5000

5000 - 10000 = 5000 credit from debt.

yr 2 = 50000 x 1.10^2 = 500 debit from debt = 5000-15000= 10,000 credit from debt

yr 3 = 50000 x 1.10^3 = 50 debit from debt

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19500 paid of initial and nothing owed on interest.

50000-19500= 30,500 rupees owed + 50 rupee interest.

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4 0
2 years ago
Read 2 more answers
Need help for this please
EastWind [94]
The perimeter is about 82 yards

first, the perimeter of the rectangles is 30*2 = 60 (the 7 is not a part of the overall perimeter so we do not need to add it)

the "perimeter" (circumference) of the 2 semi circles = (22/7)*7 = 22by using the formula C = pi*d (2 semi circles of the same diamter = 1 circle)

now just add the 2 answers
22 + 60

= 82 yards
4 0
2 years ago
6 There were 35 children and 10 adults at a cookout. What is the ratio of children to total people at the cookout?
Grace [21]
7:9 because there are 35 children and 10 adults. Add 35 and 10 you get 35:45 then you simplify the ratio to get 7:9.
6 0
3 years ago
The measure of&lt;ABC is 102°, find the measure of &lt;DBC
mylen [45]
Yes you are right because will be 102 - 52 = 50 degrees 
4 0
3 years ago
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