Question

Find the height of a cylinder whose volume is 38.5^3and it's diameter of base is 3.5 cm please answer the question with step by step explaination please answer fast ​

Answer 1

Solution :

Given:

• Volume of cylinder = 38.5cm³.
• Diameter of base of cylinder = 3.5cm.

To find:

• The height of a cylinder.

Explanation:

We know that, if we are given with the diameter of base of cylinder, we have the required formula, that is,

• Radius = Diameter/2.

By using the required formula to calculate the radius of cylinder and substituting the given values in the formula, we get:

→ Radius = 3.5/2

→ Radius = 1.75.

Now,

We know that, if we are given with the volume of cylinder and radius of cylinder, we have the required formula, that is,

• Volume of cylinder = πr²h.

By using the required formula of volume of cylinder to find the height of cylinder and substituting all the given values in the formula, we get:

→ 38.5 = 22/7 ×(1.75)² × h

→ 38.5 = 22/7 × 3.06 × h

→ 38.5 × 7 = 22 × 3.06 × h

→ 269.5 = 22 × 3.06 × h

→ 269.5 = 67.32 × h

→ 269.5 = 67.32h

→ h = 269.5/67.32

→ h = 4.003 (Approx)

Hence, the height of a cylinder is 4.003cm approximately.

Answer 2

Answer:

Given :-

• A cylinder whose volume is 38.5 m³ and it's diameter is 3.5 cm.

To Find :-

• What is the height of a cylinder.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Volume\: Of\: Cylinder =\: {\pi}{r}^{2}h}}}$

where,

• r = Radius
• h = Height

Solution :-

First, we have to find the radius of a cylinder :

As we know that,

$\longmapsto \sf\boxed{\bold{\pink{Radius =\: \dfrac{Diameter}{2}}}}$

Given :

• Diameter = 3.5 cm

According to the question by using the formula we get,

↦ $\sf Radius =\: \dfrac{3.5}{2}$

➦ $\sf\bold{\green{Radius =\: 1.75\: cm}}$

Now, we have to find the height of a cylinder :

Let, the height of a cylinder be x cm

Given :

• Radius = 1.75 cm
• Volume of a cylinder = 38.5 m³

According to the question by using the formula we get,

↦ $\sf {\pi}{r}^{2}h =\: 38.5$

↦ $\sf \dfrac{22}{7} \times {(1.75)}^{2} \times h =\: \dfrac{385}{10}$

↦ $\sf \dfrac{22}{7} \times 3.06 \times h =\: \dfrac{385}{10}$

↦ $\sf \dfrac{22}{7} \times \dfrac{306}{100} \times h =\: \dfrac{385}{10}$

↦ $\sf h =\: \dfrac{385 \times 7 \times 10\cancel{0}}{1\cancel{0} \times 22 \times 306}$

↦ $\sf h =\: \dfrac{385 \times 7 \times \cancel{10}}{\cancel{22} \times 306}$

↦ $\sf h =\: \dfrac{\cancel{385} \times 7 \times 5}{\cancel{11} \times 306}$

↦ $\sf h =\: \dfrac{35 \times 35}{306}$

↦ $\sf h =\: \dfrac{\cancel{1225}}{\cancel{306}}$

➠ $\sf\bold{\red{h =\: 4.003\: cm(approx)}}$

$\therefore$ The height of a cylinder is 4.003 (approx).