Question

6. If the volume of a right circular cylinder is 9πh m3, where h is its height (in meters), what is the diameter of the base of the cylinder is equal to?

Answer 1

$\LARGE{ \underline{ \orange{ \sf{Required \: answer:}}}}$

We have the volume of a cylinder and the height, so we need to find the radius first to get the diameter of the right circular cylinder.

• Volume of the cylinder = 9πh m³
• Height of the cylinder = h

Formula for finding the volume:

$\large{ \because{ \underline{ \boxed{ \rm{volume = \pi {r}^{2} h }}}}}$

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Now plugging the given values of volume of cylinder and height of the cylinder to get the radius.

⇛ πr²h = 9πh

⇛ r² = 9πh / πh

⇛ r² = 9

⇛ r = $\pm$3

Since, radius can't be negative. The measure of the radius of the circular base is 3 m.

⇛ Diameter = 2 × Radius

⇛ Diameter = 2 × 3 = 6 m

Thus, our required answer is 6 m

Answer 2

Step-by-step explanation:

$\sf \underline{Given} :$

• If the volume of a right circular cylinder is 9πh m3,

• where h is its height (in meters),

$\sf \underline{To \: Find} :$

• what is the diameter of the base of the cylinder is equal to?

$\sf \underline{Solution \: } :$

Let the radius of base be r metres :

$\underline{ \boldsymbol{According \: to \: the \: question.}} :$

the diameter of the base of the cylinder is equal :

$\therefore \sf \: \cancel{\pi} {r}^{2}\cancel{h} = 9\cancel{\pi }\cancel{h} \\ \\ \sf \leadsto \: {r}^{2} \: = 9 \\ \\ \sf \leadsto \: \: r \: = \sqrt{9} \\ \\ \sf \leadsto \: r= \underline{3}$

$\therefore \sf \leadsto \: Diameter = 2 \times 3 \\ \\ \sf \leadsto \: Diameter =6 \: m$