Solve each problem. Find the radius and height (to the nearest th...

Question

Solve each problem. Find the radius and height (to the nearest thousandth) of an open-ended cylinder with volume 50 in.^3 and lateral surface area 65 in.^2.

Accepted Answer

Hello everybody. I'm doing all right. Today, we're gonna be looking at this math question that states that the volume and the curved surface area of a right circular cylinder are 25 cubic centimeters and 40 centimeters squared respectively. And then they ask us to find the measure of the radius and the height of the cylinder while noting that the cylinder is open at both ends. Now, the answer choices that they provided are a radius of 4/ centimeters and a height of 16, divided by five centimeters. B, a radius of 5/4 centimeters and a high. The same as AC are radius, the same as B and a height of pi divided by 16 centimeters and D are radius the same as A and a high, the same as C. Now let's try to illustrate what they told us. So we have a right circular cinder. So let's draw that we'll give it a little bit like that. And for this cylinder will have a height of H A A radius R. Now, we should also note that they tell they give us the surface area and or the curved surface area and the volume So we know that curved surface area is equal to two pr H and the volume is equal to I R squared H. So with this information and with the numbers that they gave us, we can do some plugging in and some solving for different variables. So I'll be plugging into the curved surface area first. So we had that too pr H is equal to 40 centimeters squared. And I'm gonna solve for H so I'll have H equals 40 centimeters squared divided by two pi R and the 40 and the two will cancel out. So we'll have that H is equal to 20 centimeter squared divided by pr Now, we can use that H and plug it into our volume equation. So our volume equation was pi R squared H. So in this case, we'll plug that H in. So we'll have pi R squared multiplied by 20 centimeters squared divided by pi R and that will be equal to the volume which they told us was centimeters cubed. And now we have, we see that we have a pi R squared outside of the parentheses or that's multiplying a fraction with the denominator of pr so that pi R as in the denominator will cancel out the pi that's multiplying that will cancel out as well. And the R squared will cancel leaving one R. So one of the R squares will cancel. So we'll have 20 multiplied by R centimeter squared or we should have it rearranged as 20 centimeter squared, R equals centimeters cubed. And now we can solve for art. So we have that radius is equal to 25 centimeters cubed divided by 20 centimeters squared. And the centimeter squared will cancel out with two of the three centimeters on the numerator canceling out as well. And 25 divided by 20 is the same as saying five divided by four and it'll be centimeters. So 5/4 centimeters and that is equal to R. So that is one of our answers, our radius. So we can eliminate answer choice A and answer choice D right away because they have a different radius. So now we can plug that R into our high equation R H which as I'll put again was H is equal to 20 centimeters squared divided by pr so we'll plug that R in. So we'll have H is equal to 20 centimeters squared divided by pi multiplying 5/ centimeters. And when you do all that, one of the centimeters, the one of the centimeters will cancel out on both sides and you'll be left with H is equal to 16 divided by pi which will be our second answer for this question or answer choice B in this scenario. So I hope that was helpful. And until next time.

Solve each problem. Find the radius and height (to the nearest thousandth) of an open-ended cylinder with volume 50 in.^3 and lateral surface area 65 in.^2.

Key Concepts

Volume of a Cylinder

Lateral Surface Area of a Cylinder

System of Equations

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