SME
Grade 8 Math · Problem type
Change one dimension
Use this for “A cylinder holds 60π cm³. What does it hold at 3 times the height?” or “Quadruple the radius of a cone.”
Table
Height multiplied by (k)
New volume (W)
(cm³)
This is an example. Type your own values to start a new problem.
W
=
V
×
k
×
j
2
Formulas
W
=
V
×
k
×
j
2
(new
volume
=
volume
at
first
×
height
multiplied
by
×
radius
multiplied
by²)
180π
=
60π
×
3
×
1
2
Assumptions
•
Multiplying the height by k multiplies the volume by k.
•
Multiplying the radius by j multiplies the volume by j²: the radius is in the base area twice.
•
The same holds for cones; for a sphere the radius counts three times (j³).
Step-by-step
WE KNOW
V = 60π cm³ (volume at first), k = 3 (height multiplied by), j = 1 (radius multiplied by)
FIND
new volume (W)
Step 1 · Find new volume (W)
Use W = V × k × j² (new volume = volume at first × height multiplied by × radius multiplied by²)
Multiply by the height’s factor once and the radius’s factor twice.
W
=
60π
×
3
×
1
2
W
=
180π
cm³
(≈
565.49
cm³)
Check
Put the numbers back in. Both sides should match.
180π
=
60π
×
3
×
1
2
✓
Topic check
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Volume of cylinders, cones and spheres
Main lesson
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