Question

height of a right circular is twice of its radius. if the hight would be 6 times of its radius. then the volume of the cylinder would be greater by 539 cubic dem. find the hight of cylinder.​

Answer 1

✍️AnSwer:

Height of the cylinder is 7 cm.

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✒GiVen:

Here it is given that there's a cylinder whose height is twice it's radius and height is 6 times it's radius. Also, volume of the cylinder is 539 cm³.

✒To Find:

• We are supposed to find height of the cylinder.

✒SoluTion:

Let us consider the radius of cylinder be r and height of the cylinder be 2r.

If it's height is 6 times that of it's radius, then,

New height of cylinder would be 6r.

Now,

According to the question,

$\bigstar \sf \: Volume \: of \: the \: cylinder = 539 \\ \\ \longmapsto \sf \: \: \pi {r}^{2} \times 6r - \pi {r}^{2} \times 2r= 539 \\ \\ \longmapsto \sf \: \:4\pi {r}^{3} = 539 \\ \\ \longmapsto \sf \: \: {r}^{3} = \dfrac{539}{4\pi} \\ \\ \longmapsto \sf \: \: {r}^{3} = \dfrac{539 \times 7}{ 4\times22} \\ \\ \longmapsto \sf \: \: {r}^{3} = { \bigg(\dfrac{7}{2} \bigg )}^{3} \\ \\ \longmapsto \sf \: \:r = \dfrac{7}{2}$

Now, let us find height :

$\longmapsto \sf \: \:2r \\ \\ \longmapsto \sf \: \:2 \times \frac{7}{2} \\ \\ \longmapsto \sf \: \:{ \underline{ \boxed{ \bf{ \purple{ \: 7 \: cm \: }}}}} \: \bigstar$

Therefore, height of the cylinder is 7 cm.

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✍️ExPlore More :

• Surface Area of Cylinder = 2πr (h + r) sq.unit
• CSA or LSA = 2π × r × h sq. units
• TSA = 2π × r × h + 2πr² = 2πr (h + r) sq.units

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#TheVenomGirl ⚡

Answer 2

Given :

• Height of a right circular is twice of its radius of the base. if the height be 6 times of its radius. then the volume of the cylinder would be greater by 539 cm³ more.

To Find :

• Height of cylinder = ?

Solution :

Let the radius of cylinder be r and height of cylinder be 2r.

If it's height be 6 times it's radius, then the new height of cylinder = 6r

☢ According to question :

➨ πr² × 6r × πr² × 2r = 539

➨ 4πr³ = 539

➨ r³ = 539 × 7 / 4 × 22

➨ r³ = (7/2)³

➨ r = 7/2 cm

Hence, radius of the cylinder is 7/2 cm.

Height of cylinder = 2r = 2 × 7/2 = 7 cm

Therefore, the height of the cylinder is 7 cm.