Question

The base radius and height of a right circular cylinder are 5 cm and 10 cm. Its total surface area is
(a)150π sq cm
(b)300π sq cm
(c)150 sq cm
(d)300 sq cm​

Answer 1

Answer:

Total surface area of cylinder = 150π cm²

Step-by-step explanation:

Given that:

• Base radius of a right circular cylinder = 5 cm
• Height of the cylinder = 10 cm

To find:

Total surface area of cylinder.

Formula to find total surface area of cylinder:

T.S.A = 2πr(r + h) sq. unit

Where,

• T.S.A = Total surface area
• r = Radius
• h = Height

Finding the total surface area of cylinder:

• Total surface area of cylinder = 2π × 5(5 + 10) cm²
• Total surface area of cylinder = 2π × 5 × 15 cm²
• Total surface area of cylinder = 150π cm²

Answer 2

${\large{\bold{\rm{\underline{Given \; that}}}}}$

➝ Base radius of a right circular cylinder = 5 cm.

➝ Height of a right circular cylinder = 10 cm.

${\large{\bold{\rm{\underline{To \; find}}}}}$

➝ Total surface area of a right circular cylinder.

${\large{\bold{\rm{\underline{Solution}}}}}$

➝ Total surface area of a right circular cylinder = 150π sq. cm

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

➝ Formula to find TSA of cylinder

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

➝ TSA of cylinder = 2πr(r+h)

${\large{\bold{\rm{\underline{Where,}}}}}$

★ TSA denotes total surface area.

★ π is pronounced as pi

★ The value of π is 22/7 or 3.14

★ r denotes radius

★ h denotes height

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

➜ TSA of cylinder = 2πr(r+h)

➜ TSA of cylinder = 2π5(5+10)

➜ TSA of cylinder = 2π5(15)

➜ TSA of cylinder = 2 × π × 5 × 15

➜ TSA of cylinder = 2 × π × 75

➜ TSA of cylinder = 150π sq. cm

${\large{\bold{\rm{\underline{More \; knowledge}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cylinder \: = \: \pi r^{2}h}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Surface \: area \: of \: cylinder \: = \: 2 \pi rh + 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Lateral \: area \: of \: cylinder \: = \: 2 \pi rh}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Base \: area \: of \: cylinder \: = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Height \: of \: cylinder \: = \: \dfrac{v}{\pi r^{2}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: cylinder \: = \:\sqrt \dfrac{v}{\pi h}}}}$