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

$\LARGE{\red{\boxed{\purple{\underline{\blue{\underline{ \green{ \underline{\orange{\mathtt{Answer:↓}}}}}}}}}}}$

$\LARGE\bold{ \green{ \boxed{\blue{\underline{\mathtt{\green{:Solution↓}}}}}}}$

$\LARGE\bold{ \red{ \boxed{\blue{\underline{\mathtt{\red{Given:↓}}}}}}}$

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

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• The height of a cylinder.

$\LARGE\bold{ \red{ \boxed{\red{\underline{\blue{\underline{\green{\underline{\mathtt{\blue{Explanation:↓}}}}}}}}}}}$

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

$Radius = \frac{Diameter}{2}$

$\sf \bf \huge {\boxed {\mathbb {INFORMATION}}}$

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

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

→ Radius = 3.5/2

→ Radius = 1.75.

$\sf \bf \huge {\boxed {\mathbb {Now}}}$

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

$\sf \bf {\boxed {\mathbb {FORMULA}}}$

• 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:

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

• → 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)

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

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

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Area \:of \:the \:rectangle =l\times b$

$\sf Perimeter \:of \:the \:rectangle =2(l+b)$

$\sf Diagonal\:of \:the \:rectangle =\sqrt{{b}^{2}+{l}^{2}}$