163k views
4 votes
. The volume of a cylinder is 200π. If the height of the cylinder is 3 cm more than the radius, what are the dimensions of the cylinder? HINT: the formula for the volume of a cylinder is V=πr 2 h

a. radius =25 cm, height =8 cm
b. radius =5 cm, height =8 cm
c. radius =8 cm, height =5 cm
d. radius =8 cm, height =25 cm

User AnkeyNigam
by
7.5k points

1 Answer

5 votes

Final answer:

The cylinder with a volume of 200π cm³ has dimensions of a 5 cm radius and an 8 cm height, which is solved using the volume formula V = πr²h.

Step-by-step explanation:

The volume of a cylinder is given by the formula V = πr²h, where V is volume, r is radius, and h is height. Given the volume of the cylinder as 200π cm³, and the height being 3 cm more than the radius, we can set up the equation 200π = πr²(h), and h = r + 3. Simplify this to 200 = r²(r + 3).

We then solve the cubic equation. The correct dimensions that satisfy this equation are a radius of 5 cm and a height of 8 cm (since 5²(5 + 3) = 200). Thus, we find that with a radius of 5 cm and a height of 8 cm, the given volume of the cylinder is achieved. Option (b) is the correct answer.

User Michel Milezzi
by
9.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories