Question

Find the volume of the cylinder if the
circumference of the cylinder is 132
cm and height is 25 cm.
3m​

Answer 1

Given :

• Circumference of the cylinder = 132 cm
• Height of the cylinder = 25 cm

To find :

• Volume of cylinder

Concept :

Firstly, we will calculate the radius of the cylinder by using the formula of circumference. After getting value of radius substitue the value of height and radius in the formula of volume of cylinder. The resultant value will be our required answer.

➳ Formula of circumference :-

• Circumference = 2πr

➳ Formula to calculate volume of cylinder :-

• Volume of cylinder = πr²h

where,

• Take π = 22/7
• r stands for the radius
• h stands for the height

Solution :

Radius of the cylinder :-

Using formula,

★ Circumference = 2πr

Substituting the given values,

→ 132 = 2 × 22/7 × r

→ Multiplying 2 by 22.

→ 132 = 44/7 × r

→ Transposing 44/7 to the other side. As 44 was the numerator and 7 was the denominator, on transposing 44 and 7 will become denominator and numerator respectively.

→ 132 × 7/44 = r

→ 66 × 7/22 = r

→ 33 × 7/11 = r

→ 3 × 7 = r

→ 21 = r

Radius of the cylinder = 21 cm

Volume of cylinder :-

Using formula,

★ Volume of cylinder = πr²h

Substituting the given values,

→ Volume = 22/7 × (21)² × 25

→ Volume = 22/7 × 21 × 21 × 25

→ Volume = 22 × 3 × 21 × 25

→ Volume = 34,650

Therefore,

• Volume of the cylinder = 34,650 cm³

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KNOW MORE :

• Surface area of cylinder = 2πrh + 2πr² or 2πr(h + r)
• Base area of cylinder = πr²
• Lateral area of cylinder = 2πrh

Answer 2

${ \large{ \underline{ \underline{ \pmb{ \sf{Given...}}}}}}$

● The circumference of the cylinder is 132cm

● The hieght of the cylinder is 25cm

${ \large{ \underline{ \underline{ \pmb{ \sf{To \: Find...}}}}}}$

● The volume of the cylinder

${ \large{ \underline{ \underline{ \pmb{ \sf{Let's\: understand\:the\: concept...}}}}}}$

● Here, we have the circumference and the hieght of the cylinder so, we have to find the radius of the cylinder form the circumcircumference given. As we already have the hieght we can find the volume of the cylinder.

${ \large{ \underline{ \underline{ \pmb{ \sf{Let's\: Use \: concept...}}}}}}$

✪ Formula to find the circumference of a circle is 2πr

✪ Formula to find the volume of a cylinder is πr²h

${ \large{ \underline{ \underline{ \pmb{ \sf{Calculation..}}}}}}$

● Now let's find the radius of the circle

★ We know,

• Circumference = 132cm

★ Now,

${ : \implies} \sf 2 \pi r = 132cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { : \implies} \sf 2 \times \frac{22}{7} \times r = 132cm$

➛Transposing terms to find the value of radius

${ : \implies} \sf r = \frac{132 \times 7}{2 \times 22} \\ \\{ : \implies} \sf r = \frac{66 \times 7}{22} \: \: \\ \\ { : \implies} \sf r = 3 \times 7 \: \: \: \: \: \\ \\ { : \implies} \sf \: r = { \underline{ \boxed{ \frak{21cm}}} \star}$

• Henceforth the measure of the radius is 21cm

● As we have found the radius now let's find the volume

★ We know,

• Volume = πr²h

★ Now,

${ : \implies} \sf volume = \pi {r}^{2} h \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { : \implies} \sf volume = \frac{22}{7} \times {(21)}^{2} \times 25 \\ \\ { : \implies} \sf volume = 22 \times 3 \times 21 \times 25 \\ \\ { : \implies} \sf volume = 34650 {cm}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the volume of the cylinder is 34,650cm³

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