Find the height of the ice cream left in the conical container
If the volume is half the volume of the container

This one is very easy guys kill it

I can't solve anything again today..

for this one; this is volume of similar shapes..

first calculate the height and volume of the conical container.. then half of the volume of the container is the volume of the ice cream left..

we use those three parameters to determine the height of the ice cream. thank you and good night

dejt4u:
I can't solve anything again today..

for this one; this is volume of similar shapes..

first calculate the height and volume of the conical container.. then half of the volume of the container is the volume of the ice cream left..

we use those three parameters to determine the height of the ice cream. thank you and good night

Smile good night
But tomorrow try and do the working as you just explained,
You might experience some difficulty to get the height,
Looking forward to seeing your solution

ifada123:
Find the height of the ice cream left in the conical container
If the volume is half the volume of the container

answer is 12.7cm

using the formula V =⅓×πr²h to find the height of the conical container, h = 16cm

now; for volume similar shapes, (V1/V2) = (h1/h2)³,
V1 = volume of the container,
V2 = volume of the ice cream,
h1 = height of the container, and
h2 = height of the ice cream

but (V1/V2) = 2 (since the volume of ice cream is half the volume of the container)

therefore, (h1/h2)³ = 2,
remember, h1 = 16cm

then, h2 = 12.7cm


**updated

dejt4u:
answer is 13.564

using the formula V =⅓×πr²h to find the height of the conical container, h = 17.09.

now; for volume similar shapes, (V1/V2) = (h1/h2)³,
V1 = volume of the container,
V2 = volume of the ice cream,
h1 = height of the container, and
h2 = height of the ice cream

but (V1/V2) = 2 (since the volume of ice cream is half the volume of the container)

therefore, (h1/h2)³ = 2,
remember, h1 = 17.09

then, h2 = 13.564

Not correct volume scale factor is different from linear scale factor,

This question is still open for possible solution no one has got it yet

h = 16 ÷ (2)^⅓ ≈ 12.6992084 units

Okay, let me solve it

Martinez39:


h = 16 ÷ (2)^⅓ ≈ 12.6992084 units

√√√√√√√√
Correct

See solution

ifada123:

√√√√√√√√
Correct

I gave myself unnecessary stress.. I thought the h given is slant height (l)

dejt4u:
I gave myself unnecessary stress.. I thought the h given is slant height (l)

Smile

The answer is 12.69.


1) Linear scale factor (LSF) = Big/Small
H= height of cone =16cm
h= height of ice cream.

LSF = H/h= 16/h

2) Volume Scalt Factor = LSF cubed.
v= volume of ice cream=1

V= volume of cone=2


However, v= LSF cubed* V
v= (16/h) cubed* V

Since v is half of V, then. v/V=1/2

Therefore 1/2= 16/h cubed
=> h cubed= 16*16*16/2
h cubed= 2048

h= cube root of 2048= 12.69

Therefore, the height of ice cream is roughly 12.7 cm

oyatz:
The answer is 12.69.


1) Linear scale factor (LSF) = Big/Small
H= height of cone =16cm
h= height of ice cream.

LSF = H/h= 16/h

2) Volume Scalt Factor = LSF cubed.
v= volume of ice cream=1

V= volume of cone=2


However, v= LSF cubed* V
v= (16/h) cubed* V

Since v is half of V, then. v/V=1/2

Therefore 1/2= 16/h cubed
=> h cubed= 16*16*16/2
h cubed= 2048

h= cube root of 2048= 12.69

Therefore, the height of ice cream is roughly 12.7 cm

√√√√√√√√√√√√ correct

r:h = 3:8
R= 6
H= 16

Big cone vol = 2 small cone vol

Therefore, 1/3 π R²H=2(1/3 π r²h)

R²H = 2r²h

h =36*16 ÷ 2 r²

h = 576 ÷ 2(3h/8 ) ²

h = 576 ÷ 9h²/32

h = 576*32/9h²

h³ = 576*32/9

h =12.6999cm