Question

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Question:-

Q. The height of a cone is 16cm and its base radius is 12cm. Find the curved surface area and the total surface area of the cone (Use π = 3.14).

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Answer 1

Step-by-step explanation:

hyy bro

here h= 16

r= 12

π=3.14

l = √h²+√r²

= √16² + √12²

= √256 + √144

= √400

= 20cm

curved surface area = πrl

=3.14 ×12×20

=314/100×12×20

=753.6cm²

total surface area of cone = πr(r+l)

= 3.14×12(12+20)

= 314/100×12 ×32

= 1204.56cm²

hope it helps uh

Answer 2

${\large{\bold{\bf{\sf{\underline{Understanding \; the \; question}}}}}}$

➨ This question says that there is a cone given it's height is 16 cm an it's base radius is 12 cm. Now we have to find the curved surface area and the total surface area of the cone. Also this question says that we have to use 3.14 at the place of π

${\large{\bold{\bf{\sf{\underline{Given \; that}}}}}}$

➨ Height of cone = 16 cm.

➨ Base radius of cone = 12 cm.

${\large{\bold{\bf{\sf{\underline{To \; find}}}}}}$

➨ Curved Surface area of the cone

➨ Total surface area of the cone.

${\large{\bold{\bf{\sf{\underline{Solution}}}}}}$

➨ Curved Surface area of the cone = 753.6 cm²

➨ Total surface area of the cone = 1205.76 cm²

${\large{\bold{\bf{\sf{\underline{Using \; concepts}}}}}}$

➨ Curved Surface area of the cone formula

➨ Total surface area of the cone formula

${\large{\bold{\bf{\sf{\underline{Using \; formulas}}}}}}$

➨ Curved Surface area of the cone = πrl

➨ Total surface area of the cone = πr(r+l)

${\large{\bold{\bf{\sf{\underline{We \: also \: write \: these \: as}}}}}}$

➨ π pronounced as pi

➨ Value of π is 3.14 or 22/7

➨ r denotes Radius

➨ l denotes length

➨ CSA also written as Curved Surface Area

➨ TSA also written as Total surface Area

${\large{\bold{\bf{\sf{\underline{Small \; procedure}}}}}}$

➨ To solve this problem 1st part we have to use the formula to find curved surface area of cone putting the values we get 753.6 cm² as surface area of cone. Now solving 2nd part we have to use the formula to find total surface area of cone putting the values we get 1025.76 cm² as total surface area of cone. Hence, we have done ✓

${\large{\bold{\bf{\sf{\underline{Full \: Solution}}}}}}$

~ Finding length

${\bold{\sf{l = \sqrt{16 ^{2} + {12}^{2}}}}}$

${\bold{\sf{l = \sqrt{226 + 144}}}}$

${\bold{\sf{l = \sqrt{400}}}}$

${\bold{\sf{l = 20}}}$

• Henceforth, 20 cm is the length of the given cone.

~ Finding Curved surface area of the cone

➥ CSA = πrl

➥ CSA = 3.14(12)(20)

➥ CSA = 3.14 × 12 × 20

➥ CSA = 3.14 × 240

➥ CSA = 753.6 cm²

• Henceforth, CSA ( Curved Surface Area ) of the cone is 753.6 cm²

~ Finding Total surface area of the cone

➥ TSA = πr(r+l)

➥ TSA = 3.14 × 12 (12+20)

➥ TSA = 3.14 × 12 × 32

➥ TSA = 3.14 ×

➥ TSA = 1205.76 cm²

• Henceforth, TSA ( Total surface area ) of the cone is 1205.76 cm²

${\large{\bold{\bf{\sf{\underline{More \; knowledge}}}}}}$

Formulas related to cone –

$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}$

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