Question

find the volume, CSA, TSA of right circular cylinder with base radius 14 cm, height 35 cm​

Answer 1

Answer:

Given :-

• A right circular cylinder with base radius 14 cm, height 35 cm.

To Find :-

• What is the volume, curved surface area (CSA), total surface area (TSA) of circular cylinder.

Formula Used :-

♣ Volume Formula :

★ Volume = πr²h ★

♣ Curved Surface Area or CSA Formula :

★ Curved Surface Area = 2πrh ★

♣ Total Surface Area or TSA Formula :

★ Total Surface Area = 2πr(r + h) ★

where,

• π = pie or 22/7
• r = Radius
• h = Height

Solution :-

❒ In case of volume of right circular cylinder :

Given :

• Radius (r) = 14 cm
• Height (h) = 35 cm

According to the question by using the formula we get,

↦ Volume = πr²h

↦ Volume = 22/7 × (14)² × 35

↦ Volume = 22/7 × 14 × 14 × 35

↦ Volume = 22/7 × 196 × 35

↦ Volume = 22/7 × 6860

↦ Volume = 22 × 980

➠ Volume = 21560 cm³

∴ The volume of right circular cylinder is 21560³ .

❒ In case of curved surface area or CSA of right circular cylinder :

Given :

• Radius (r) = 14 cm
• Height (h) = 35 cm

According to the question by using the formula we get,

↦ Curved Surface Area = 2πrh

↦ Curved Surface Area = 2 × 22/7 × 14 × 35

↦ Curved Surface Area = 44/7 × 490

↦ Curved Surface Area = 44 × 70

➠ Curved Surface Area = 3080 cm²

∴ The curved surface area or CSA of right circular cylinder is 3080 cm² .

❒ In case of total surface area or TSA of right circular cylinder :

Given :

• Radius (r) = 14 cm
• Height (h) = 35 cm

According to the question by using the formula we get,

↦ Total Surface Area = 2πr(r + h)

↦ Total Surface Area = 2 × 22/7 × 14(14 + 35)

↦ Total Surface Area = 44/7 × 14(49)

↦ Total Surface Area = 44/7 × 14 × 49

↦ Total Surface Area = 44/7 × 686

↦ Total Surface Area = 44 × 98

➠ Total Surface Area = 4312 cm²

∴ The total surface area or TSA of right circular cylinder is 4312 cm² .

Answer 2

$\large \bf \clubs \:  Given :-$

For A Right Circular Cylinder :

• Base Radius , r = 14 cm

• Height , h = 35 cm

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$\large \bf \clubs \:  To \: Find :-$

${\begin{cases} \: \: \text{CSA \: of \: Cylinder } \\ \text{ TSA \: of \: Cylinder } \\ \text{ Volume \: of \: Cylinder} \end{cases}}$

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$\large \bf \clubs \:  Main \: Formulas :-$

${\begin{cases} \: \: \text{CSA \: of \: Cylinder } = 2\pi \text{rh}\\ \text{ TSA \: of \: Cylinder } = 2\pi \text{r(r + h)} \\ \text{ Volume \: of \: Cylinder} = \pi {r}^{2} \text{h} \end{cases}}$

Where ,

• r = Base Radius of Cylinder

• h = height of Cylinder

• $\pi = \dfrac{22}{7}$

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$\large \bf \clubs \:  Solution :-$

We Have ,

• r = 14 cm

• h = 35 cm

✏ Calculating CSA of Cylinder :

Using Formula of CSA

$\text{CSA =2πrh } \\ \\ = 2 \times \frac{22}{7} \times 14 \times 35 \\ \\ =44\times70\\\\ \purple{ \Large :\longmapsto  \underline {\boxed{{\bf CSA = 3080 cm^2} }}}$

✏ Calculating TSA of Cylinder :

Using Formula of TSA

$\text{TSA =2πr(r + h) } \\ \\ = 2 \times \frac{22}{7} \times 14 (14 + 35)\\ \\ =2 \times \frac{22}{7} \times 14 \times 49\\\\ \purple{ \Large :\longmapsto  \underline {\boxed{{\bf TSA = 4312 cm^2} }}}$

✏ Calculating Volume of Cylinder :

Using Formula of Volume

$\text{Volume =πr²h } \\ \\ = \frac{22}{7} \times (14 {)}^{2} \times 35 \\ \\ =\frac{22}{7} \times 196\times 35 \\\\ \purple{ \large :\longmapsto  \underline {\boxed{{\bf Volume = 21560 cm^3} }}}$

Hence ,

$\pink{{\begin{cases} \: \: \bf{CSA \: of \: Cylinder }=3080cm^2 \\ \bf{ TSA \: of \: Cylinder }=4312 cm^2 \\ \bf{ Volume \: of \: Cylinder}=21560cm^3 \end{cases}}}$