Acylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm. what is the height of the cone

Volume of cylinder(V) is given by:

where,

r is the radius and

h is the height of the cylinder.

Volume of cone(V') is given by:

where, r' is the radius and h' is the height of the cone.

As per the statement:

A cylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm

⇒r = 12 cm , h = 20 cm and r' = 8 cm

Since, Volume of cylinder is equal to Volume of cone.

⇒V  = V'

then;

⇒

Substitute the given values to solve for h' we have;

⇒

Multiply both sides by 3 we have;

⇒

⇒

Divide both sides by 64 we have;

or

h' = 135 cm

Therefore, the height of the cone is, 135 cm

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step-by-step explanation:

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!