1. 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 full of punch 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.

Can someone walk me through this?

Question

1.	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 full of punch 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.

Can someone walk me through this?

twizttiez · Answer

@campbell_st

campbell_st · Answer

ok.... so the volume of a sphere is 

$$V = \frac{4}{3} \pi r^3$$

you need to find the radius of the bowl... 

then find the volume of the bowl, as a sphere... 

a hemisphere is 1/2 a sphere, so have the answer for the volume of the bowl. 

same formula and process for the ladle.. 

1. find the radius... 

2. find the volume of the sphere

3. halve the answer for the volume of the ladle.


last part... number of ladles = volume of bowl / volume of ladle

hope it helps

twizttiez · Answer

Thanks so much

campbell_st · Answer

glad to help

twizttiez · Answer

Wait okay so would I do 4/3*3.14*30^3=113040 

113040/2=56520 to get the volume of the bowl?

twizttiez · Answer

That's what I did and that's what I got

twizttiez · Answer

????

twizttiez · Answer

So I did all of that and my final answer came to 52.734475 and I rounded it to a whole number and got 52 obviously am I correct? ^-^

campbell_st · Answer

no, the question gives diameters... you need to halve the diameter to get the radius... 

diameter 30 cm    then radius r = 15

diameter 8 cm     then radius  r = 4 cm 

so but you'll need to recalculate the volumes.

twizttiez · Answer

Ohhhhh

twizttiez · Answer

Okay :"(

campbell_st · Answer

sorry about that... 

halve each volume to get the hemisphere...

twizttiez · Answer

Okay I understand so do what I did just use different numbers? XD

twizttiez · Answer

So this time use 4/3*3.14*15^2=942

942/2=471?

campbell_st · Answer

ok... here is what you need

Punch bowl.... and I'll halve the volume in the process

$$V =\frac{1}{2} \times( \frac{4}{3} \times 3.14 \times 15^3)$$

ladle... all in 1 volume 

$$V = \frac{1}{2} \times ( \frac{4}{3} \times 3.14 \times 4^3)$$

hope it helps..

twizttiez · Answer

OHHHHHHHHH

twizttiez · Answer

Wait that's what I did just longer XD

twizttiez · Answer

But I see it's a more simplified way thanks!

campbell_st · Answer

you just had the power wrong... things were correct otherwise.. 

so calculate the volumes

then its bowl divided by ladle... 

rough guess is something around 50...

campbell_st · Answer

yes, I tried to step you though it... rather the give you the whole thing, both methods are correct.

twizttiez · Answer

Yup yup

twizttiez · Answer

I have one more question could you help me out?