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PSYCHO15rus [73]
2 years ago
5

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate

is the height of the water changing when the height is 3m?
Mathematics
1 answer:
Lyrx [107]2 years ago
3 0

Answer:

Therefore the rate change of height is  \frac{1}{\pi} m/s.

Step-by-step explanation:

Given that a vertical cylinder is leaking water at rate of 4 m³/s.

It means the rate change of volume is 4 m³/s.

\frac{dV}{dt}=4 \ m^3/s

The radius of the cylinder remains constant with respect to time, but the height of the water label changes with respect to time.

The height of the cylinder be h(say).

The volume of a cylinder is V=\pi r^2 h

                                                 =( \pi \times 2^2\times h)\ m^3

\therefore V= 4\pi h

Differentiating with respect to t.

\frac{dV}{dt}=4\pi \frac{dh}{dt}

Putting the value \frac{dV}{dt}

\Rightarrow 4\pi \frac{dh}{dt}=4

\Rightarrow \frac{dh}{dt}=\frac{4}{4\pi}

\Rightarrow \frac{dh}{dt}=\frac{1}{\pi}

The rate change of height does not depend on the height.

Therefore the rate change of height is  \frac{1}{\pi} m/s.

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Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of pape
jenyasd209 [6]

Answer:

C. About 75 in²; Aubrey found the surface area of the cone and included the base.

Step-by-step explanation:

In the questions above we were given the following:

Cone with

Diameter(D) = 6 inches

Slant height (l) = 8 inches.

Aubrey made an error in her calculation.

She found the Total Surface area of the cone using the formula:

Total Surface Area of a cone = πrl + πr²

= πr(l + r)

The Total surface area of a cone is the calculated as Sum of the curved surface area of a cone and the base of the cone.

Where:

Curved surface area of the cone is calculated as = πrl

Base of a cone is calculated as = πr²

Where r = radius of the cone

l = slant height of the cone

In the question, we were given

slant height(l) = 8 inches.

radius = Diameter ÷ 2 = 6÷2 = 3 inches.

Using π = 3.14

Surface area = 3.14 × 3(8+3)

= 9.42 × 11

Surface area = 103.62 in²

Approximately to the nearest inch = 104 in² or 104 square inches.

But this answer is WRONG.

The RIGHT FORMULA Aubrey should have used is

Curved Surface Area or the Lateral Area of a Cone = πrL

slant height(l) = 8 inches.

radius = Diameter ÷ 2 = 6÷2 = 3 inches.

Using π = 3.14

Curved Surface Area of a Cone = πrL

= 3.14 × 3 inches × 8 inches

= 75.36 square inches or 75.36in²

Approximately to the nearest inch = 75 square inches or 75 in².

This is the correct answer.

The error Aubrey made was she calculated the Total surface area of the cone which includes the base of the cone instead of calculating the curved surface area of the cone only.

Hence, from the above calculation , we can see that Option C "About 75 in²; Aubrey found the surface area of the cone and included the base" is the correct option.

5 0
2 years ago
Gemma’s mum runs the merchandise shop. She buys 60 t-shirts from the wholesaler at £13 each. She sets the selling price of each
SashulF [63]

Answer:

132.6 profit

Step-by-step explanation:

13 plus 30 percent

$16.9 times 40

$676

16.9 - 30%

$11.83 times 20

$236.6 plus 676

$912.6 - 13 × 60

$912.6 - $780

132.6 profit

3 0
2 years ago
If the velocity of a car 45km/h Wes how far can it travel in 0.5 hours
juin [17]
This question asks what is half of 45.
45 divided by two equals 22.5
The car will travel 22.5 miles in .5 hours.
5 0
3 years ago
Read 2 more answers
Helllppp plzzzzzzzzzzz
kolbaska11 [484]

Answer:

A: 5

B: 32

C: 3

D; 14

C: 0.333

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
A father’s age now is three times the age that his son was 4 years ago. In
Mice21 [21]
Let ‘s’ be the son’s age 12 years ago.
Let ‘f’ be the father’s current age.

4 years ago, the son was:

s-4

So, his father is currently:

3(s-4)

=

3s-12

Therefore:

f = 3s-12

In twelve years, the son will be:

s+12

And the father will be:

f+12

This can also be written as:

3s-12+12 as the fathers younger age would be f = 3s+12

=

3s

So, we know that s+12 is half the fathers current age, meaning the father is currently 2(s+12) which is equivalent to 2s+24. Also, we know that the father is currently 3 times the sons age 12 years ago, so 3s (proven by the calculations we made above). Therefore, 2s+24=3s which means 24=s. We can then substitute this, and we will receive 24+12 = 36

Son’s current age: 36

We then substitute the son’s age 12 years ago into 2s+24 to give us the father’s age.

2(24)+24 = 72

Father’s current age: 72










7 0
1 year ago
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