Question

100 POINTS! FULLY CORRECT AND EXPLANITORY ANSWERS OLNY!

Akari has a punch bowl with a volume of 130,000/3 π cm^3. She is hosting a party where she’ll be offering guests two different sizes of cylindrical cups.




The bowl is completely full when Akari begins serving the punch.



Note: 1 cm^3=1 mL



A. Cup A has a diameter of 10 cm. and a height of 20 cm. Find Volume of Cup A.



B. Determine how many cups the punch bowl will fill using Cup size A.

Round the number of scoops to the nearest whole number, and make certain to show your work.



C. Cup B has a diameter of 20 cm. and a height of 20 cm. Find the volume of B.



D. Determine how many cups of punch the punch bowl will fill using Cup size B. Round the number of scoops to the nearest whole number, and make certain to show your work.



THIS QUESTION HAS 4 PARTS (A,B,C, and D) REMEMBER TO ANSWER THEM ALL! Thank you!

Answer 1

#1

Diameter=10cm

• Radius=r=5cm
• Height=20cm=h

`\\ \rm\Rrightarrow V=\pi r^2h`

`\\ \rm\Rrightarrow V=\pi 25(20)`

`\\ \rm\Rrightarrow V=500\pi cm^3`

#2

Total cups:-

• 130000/3π÷500π =87cups

#3

• Radius=r=10cm
• Height=20cm

`\\ \rm\Rrightarrow V=\pi 100(20)`

`\\ \rm\Rrightarrow V=2000\pi cm^3`

#4

Total cups

• 130000/3 π÷2000π=22cups

Answer 2

volume of a cylinder =
`\pi r^2h` (where r is the radius and h is the height)

diameter =
`2r` (where r is the radius)

A) volume of Cup A =
`\pi * 5^2*20=500\pi \textsf{ cm}^3`

B) Assuming the volume of the punch bowl is
`(130000)/(3)\pi \textsf{ cm}^3`

`\implies (130000)/(3)\pi / 500\pi=(260)/(3)=87 \textsf{ (nearest whole number)}`

C) volume of Cup B =
`\pi * 10^2*20=2000\pi\textsf{ cm}^3`

D) Assuming the volume of the punch bowl is
`(130000)/(3)\pi \textsf{ cm}^3`

`\implies (130000)/(3)\pi / 2000\pi=(65)/(3)=22 \textsf{ (nearest whole number)}`