Grandma Edith uses her big punch bowl at family gatherings. The bowl is half of a sphere, with a diameter of 30 cm. Her ladle is also half of a sphere, with a diameter of 8 cm. How many ladles can Grandma Edith scoop from the punch bowl? use 3.14 to approximate pi and express your answer as a whole number. show your work.

Answers

Answer 1

Answer: Our first instinct is to go through every step ...

-- calculate the volume of the bowl
-- calculate the volume of the ladle
-- divide the volume of the bowl by the volume of the ladle

and we may even start down that path. But we soon realize that
it's going to be painful and take a lot of time. So we stop right
where we are, and consider our options.
We have two options:
      #1). Give up, quit, and walk away.
      #2). Find a smarter way to do it.

Look at the formula for the volume of a sphere:

   Volume = (4/3 π) (radius³) .

Do you see that ? The radius³ is a factor in the volume of
everysphere. That means that if you multiplythe radius
of a sphere by (a number),the volume of the sphere gets
multiplied by (the same number)³ !

How does that help us with this problem ? Well, it alsomeans
that the ratio of the volumes of two spheres is

   (the ratio of their radii)³.

Radius of the bowl = 15 inches
Radius of the ladle = 4 inches
Ratio of their radii = (15/4) = 3.75

   So the bowl holds (3.75)³ as much as the ladle holds.

   (3.75)³ = 52.73 ...

   The bowl holds 52.73 ... times as much as the ladle.

   After Grandma Edith scoops 52 ladle-fulls from the bowl,
there will be less than 1 ladle-full remaining in there.

And we did it all without even knowing π .

Answer 2

Answer: 1) we calculate the volume of the big punch bowl
Volume (half sphere)=(1/2)(4/3)πr³=2/3πr³
radius=30 cm / 2=15 cm

Volume=(2/3)π(15 cm)³=2250π cm³

2) we calculate the volume of the ladle:
radius=8 cm/2=4 cm
Volume=(2/3)π(4 cm)³=128π/3 cm³

3) we calculate the number of ladles by the rule of three.
1 ladle----------------------128π/3 cm³
x------------------------------2250π cm³

x=(1 ladle * 2250π cm³) / (128π/3 cm³)=52.73 ladles≈52 ladles

Answer: 52 ladles.

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Answers

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Answers

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The lengths of the sides of the base of a right square pyramid are 2 m, and the slant height of the pyramid is 9 m. If the sides of the base and the slant height are each multiplied by 4, by what factor is the surface area multiplied? A. 8 B. 16 C. 18 D. 36

Answers

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Step-by-step explanation: If both the length of the base and the slant height of a right sqaure pyramid are multiplied by a factor of 'K' the Surface area of the pyramid is multiplied by a factor of 'K' ²

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Im sorry im many months late but hopefully this can help someone else.

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Step-by-step explanation:

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Answers

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Ben needs to buy orange juice. He can buy 64 fl oz at the grocery store for $2.00, or he can buy 256 fl oz at the wholesale club for $7.50| a) Find the unit price for the grocery store orange juice. Round your answer to the nearest thousandth.| b) Find the unit price of the wholesale club orange juice. Round your answer to the nearest thousandth.| c) Where should ben buy orange juice ifhe wants the best deal? Explain.

Answers

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Answers

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