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2 years ago

What is the volume of a hemisphere with a diameter of 61.5cm?

Mathematics

1 answer:

melamori03 [73]2 years ago

4 0

Answer:

60897cm³ (5sf)

Step-by-step explanation:

Radius = 61.5 ÷ 2 = 30.75cm

Volume of sphere = 4πr³/3

Hemisphere's volume = (4π(30.75)³ ÷ 3) ÷ 2 = 60897cm³ (5sf)

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A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

2 years ago

I want these answered please I don't have that much time.

True [87]

Download photo math and it will let you take a picture of the equation and answer it for you

6 0

2 years ago

Read 2 more answers

If g(x) = 2x + 1 and fog (x)=6x-2, find f(x).

Nostrana [21]

Answer:

$g(x) = f(x) \\ 2x + 1 = 6x - 2 \\ 2x - 6x = - 2 - 1 \\ - 4x = - 3 \\ x = \frac{3}{4}$

6 0

1 year ago

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Jada purchases a sweater for $36. The store charges her 8% sales tax on the purchase. How much sales tax will the store charge o

dusya [7]

Answer:

Step-by-step explanation:

36/100=0.36 - 1%

8*0.36=2.88$

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2 years ago

Is y = 0.860x + 3.302 a linear function?

gulaghasi [49]

Answer:

yes

Step-by-step explanation:

Yes. The given function has the form y = mx + b, which is that of a linear function. Here the slope, m, is 0.860, and the y-intercept is 3.302.

8 0

2 years ago