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3 years ago

Find the volume of a sphere with a DIAMETER of 12 cm.

Mathematics

1 answer:

Fofino [41]3 years ago

6 0

Volume of a sphere = 4/3pi*r^3
diameter/2 = radius
Radius = 12/2 =6
Volume of sphere = 4/3pi*6^3 = 288pi

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A company plans to manufacture a rectangular bin with a square base, an open top, and a volume of 13,500 in3. Determine the dime

Artyom0805 [142]

Answer:

Dimensions 30 in x 30 in x 15 in

Surface Area = 2,700 in²

Step-by-step explanation:

Let 'r' be the length of the side of the square base, and 'h' be the height of the bin. The volume is given by:

$V=13,500=h*r^2\\h=\frac{13,500}{r^2}$

The total surface area is given by:

$A=4*hr+r^2$

Rewriting the surface area function as a function of 'r':

$A=4*\frac{13,500}{r^2} *r+r^2\\A=\frac{54,000}{r}+r^2$

The value of 'r' for which the derivate of the surface area function is zero, is the length for which the area is minimized:

$A=54,000*r^{-1}+r^2\\\frac{dA}{dr}=0= -54,000*r^{-2}+2r\\\frac{54,000}{r^2}=2r\\ r=\sqrt[3]{27,000}\\r=30\ in$

The value of 'h' is:

$h=\frac{13,500}{30^2}\\ h=15\ in$

The dimensions that will ensure the minimum surface area are 30 in x 30 in x 15 in.

The surface area is:

$A=4*15*30+30^2\\A=2,700\ in^2$

3 0

3 years ago

The equation of a circle is (x−2)^2+(y−16)^2=169 . What is the circle's radius?

Svetllana [295]

Hello!

The equation for a circle is

$(x-h)^{2} +(y-k)^{2} = r^{2}$

r is the radius

To find the radius we take the square root of the number in the radius spot

sqrt169 = 13

The answer is 13

Hope this helps!

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3 years ago

564 in scientific notation

MAXImum [283]

Answer: 5.64 *10^2

Step-by-step explanation:

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The right triangle on the right is a scaled copy of the right triangle on the left. Identify

hodyreva [135]

Answer:

scale factor : 3.5

Step-by-step explanation:

56/16=3.5

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2 years ago

True or false? "If two angles form a linear pair, they must be supplementary?"

vodka [1.7K]

Answer:

true?

Step-by-step explanation:

im guessing.

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3 years ago

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