Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

This is one of the questions for an assignment for geometry. The thing is, the lesson did not cover how to combine equations into one. The one I picked may be wrong, but could someone explain this to me please?

Relevance
• 2 months ago

The equation for the volume of a cylinder is:

V = πr²h

The equation for the volume of a cone is:

V = πr²h / 3

If the height of the cylinder is 3 times the height of the cone, then our equations come to:

V = πr²(3h) and V = πr²h / 3

The total volume is the sum of the two expressions:

πr²(3h) + πr²h / 3

Simplify the first term:

3πr²h + πr²h / 3

Common denominator:

9πr²h / 3 + πr²h / 3

(9πr²h + πr²h) / 3

And simplify:

10πr²h / 3

which can also be written as:

(10/3)πr²h

• 2 months ago

volume of cylinder = πr²h

Cone volume V = ⅓πr²h, h is height of cone (not slant)

in this case

volume of cylinder = πr²3h

volume of cone = ⅓πr²h

total volume = 3πr²h + ⅓πr²h

total volume = (9/3)πr²h + ⅓πr²h = (10/3)πr²h

• 2 months ago

the cone and the cylinder both have the same radius

- this is clear in the picture, r for the cylinder = r for the cone

the height of the cylinder is 3 times the height of the cone

- this is also clear in the picture, the height of the cone is h, the height of the cylinder is 3h

finding the total volume

Total volume = volume of cone + volume of cylinder

volume of cone = 1/3 pi Rcone-squared Hcone

volume of cylinder = pi Rcylinder-squared Hcylinder

Rcone = Rcylinder = r

Hcone = h

Hcylinder = 3h

plugging those values into the previous equations, we get

volume of cone = 1/3 pi r-squared h

volume of cylinder = pi r-squared 3h = 3 pi r-squared h

total volume = 1/3 [pi r-squared h] + 3 [pi r-squared h]

= 3+1/3 [pi r-squared h]

= 10/3 [pi r-squared h]

= 10/3 pi r-squared h