Question

find the total surface area of a cone if it is a slant height is 15cm and diameter of its base is 14cm​

Answer 1

• Total surface area of cone is 484 cm².

Step-by-step explanation:

Given :-

• Slant height of cone is 15 cm.
• Diameter of its base is 14 cm.

To find:-

• Total surface area of cone.

Solution:-

Total surface area of cone = πrl + πr².

• Here, r is radius of cone and l is slant height of cone.

Radius = Diameter/2

= 14/2

= 7

Radius of cone = 7 cm.

Slant height = 15 cm.

Put r and l in formula:

$\longrightarrow$ π × 7 × 15 + π + (7)²

$\longrightarrow$ 22/7 × 7 × 15 + 22/7 + (7)²

$\longrightarrow$ 22 × 15 + 22/7 × 7 × 7

$\longrightarrow$ 330 + 22×7

$\longrightarrow$ 330 + 154

$\longrightarrow$ 484

Therefore,

Total surface area of cone is 484 cm².

________________________

More formulas of cone :

• Lateral surface area of cone = πrl.
• Volume of cone = 1/3πr² h
• Slant height of cone = √r² + h²

Answer 2

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${ \bold { \underline{\large {Given : - }}}} \:$

◍ $\sf{Slant\:height\:of\:cone(l)\:=\:15cm.}$

◍ $\sf{Diameter\:of\:it's \:base(d)\:=\:14cm.}$

${ \bold { \underline{\large{To\:Find : - }}}} \:$

◍ $\sf{Total\:surface\:area\:(TSA)\:of\:cone!}$

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$\large\boxed{\boxed{\tt{So\:let's \:do\:it\::-}}}$

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${ \bold { \underline{\large{Solution : - }}}} \:$

ωe have slant height and base diameter of cone.

To find it's total surface area (TSA) we also need height and base radius of cone.

Firsty let's find them :-

• Radius (r) :-

ㅤㅤㅤㅤㅤ$\sf{r\:=\:\dfrac{d}{2}}$

ㅤㅤㅤㅤㅤ$\sf{r\:=\:\dfrac{14}{2}}$

ㅤㅤㅤㅤㅤ$\sf{r\:=\:\cancel{\dfrac{14}{2}}}$

ㅤㅤㅤㅤㅤ$\sf{r\:=\:7}$

$\boxed {\frak {\therefore \purple {Base\:radius\:of\:cone\:\leadsto\:7cm}}}\:\orange\bigstar$

Now, we have all values!

So, let's find total surface area (TSA) of cone!

$\sf{\red \dag \underbrace{Total\:surface\:area(TSA)_{(Cone)}\:=\:\pi r(l\:+\:r)}}\red\dag$

Let's put all values!

$\longmapsto$ $\sf{\pi\:\times\:r(l\:+\:r)}$

$\longmapsto$ $\sf{\dfrac{22}{7}\:\times\:7(15\:+\:7)}$

$\longmapsto$ $\sf{ \dfrac{22}{\cancel{7}}\:\times\: \cancel{7}\:\times\:22}$

$\longmapsto$ $\sf{22\:\times\:22}$

$\longmapsto$ $\sf{484}$

$\boxed {\frak {\therefore \purple {Total\:surface\:area(TSA)_{(Cone)}\:\leadsto\:484cm^2}}}\:\orange\bigstar$

$\large\underline{\boxed{\bold\red{SOLVED}}}$

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★ ADDITIONAL ★

• Height (h) :-

ㅤㅤㅤㅤ$\sf{(l)^2\:=\:(r)^2\:+\:(h)^2}$

ㅤㅤㅤㅤ$\sf{(15)^2\:=\:(7)^2\:+\:(h)^2}$

ㅤㅤㅤㅤ$\sf{225\:=\:49\:+\:(h)^2}$

ㅤㅤㅤㅤ$\sf{225\:-49\:=\:(h)^2}$

ㅤㅤㅤㅤ$\sf{176\:=\:(h)^2}$

ㅤㅤㅤㅤ$\sf{(h)^2\:=\:176}$

ㅤㅤㅤㅤ$\sf{h\:=\: \sqrt{176}}$

ㅤㅤㅤㅤ$\sf{h\:=\: \sqrt{2\:\times\:2\:\times\:2\:\times\:2\:\times\:11}}$

ㅤㅤㅤㅤ$\sf{h\:=\: \sqrt{4\:\times\:4\:\times\:11}}$

ㅤㅤㅤㅤ$\sf{h\:=\: 4\sqrt{11}}$

$\boxed {\frak {\therefore \purple {Height\:of\:cone\:\leadsto\:4\sqrt{11}cm}}}\:\orange\bigstar$

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More formulas of cone :-

$\sf{\pink\bigstar\:{Lateral\:surface\:area(LSA)_{(Cone)}\:=\: πrl}}$

$\sf{\pink\bigstar\:{Volume_{(Cone)}\:=\: \dfrac{1}{3}\pi r^2 h}}$

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${ \bold { \underline{\large{Important \: Notice : - }}}} \:$

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