Question

The curved surface area of a cone is 670 and its radius is 15 then its total surface area is..​

Answer 1

Answer:

Total surface area is 1376.5 unit²

Explanation:

Given

• Curved surface area of a cone = 670 unit²
• Radius of the cone = 15 units

To Find

• Total surface area of the cone.

Solution

Curved surface area of cone = πrl = 670 unit²

Total surface area of cone = πrl + πr²

Substitute 670 unit² in place of πrl

⟹ 670unit² + πr²

⟹ 670 unit² + π ( 15unit )²

⟹ 670 unit² + π × 225 unit²

⟹ 670 unit²+ 3.14 × 225 unit²

⟹ 670 unit² + 706.5 unit²

⟹ ( 670 + 706.5) unit²

⟹ 1376.5 unit²

Total surface area is 1376.5 unit²

Answer 2

⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Question}}}}$

The curved surface area of a cone is 670 cm² and its radius is 15 cm then its total surface area is..

⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Answer}}}}$

Given:

⠀⠀

• The curved surface area of the cone is 670 cm²

• radius of the cone is ( r ) = 15 cm

⠀⠀

To find:

⠀⠀

Find the total surface area of the cone .

⠀⠀

Solution:

⠀⠀

We know that,

$\boxed{\bf{\pink{Curved\:surface\:area\:of\:cone=πrl}}}$

⠀⠀

Where,

• r = radius of the cone

• l = slant height of the cone

• π = 22/7

⠀⠀

According to the question,

⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:\implies πrl=670}$

⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:\implies \dfrac{22}{7}×15×l=670}$

⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:\implies l=670×\dfrac{7}{22}×\dfrac{1}{15}}$

⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:\implies l=670×\dfrac{7}{330}}$

⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:\implies l=\dfrac{67×7}{33}}$

⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:\implies l=\dfrac{469}{33}}$

⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:\implies l={\cancel{\dfrac{469}{33}}}}$

⠀⠀

⠀⠀⠀⠀⠀⠀$\boxed{\bf{\purple{:⟹\:l=\:14.21}}}$

⠀⠀

.°. slant height of the cone ( l ) = 14.21 cm

⠀⠀

Now,

⠀⠀

We also know that,

⠀⠀

$\boxed{\bf{\pink{total\:surface\:area\:of\:cone=πrl+πr^{2}}}}$

⠀⠀

.°. Total surface area of the cone is —

⠀⠀

⠀⠀⠀⠀$\sf{:\implies πrl+πr^{2}}$

⠀⠀

⠀⠀⠀⠀$\sf{:\implies πr(l+r)}$

⠀⠀

⠀⠀⠀⠀$\sf{:\implies \dfrac{22}{7}×15(14.21+15)\:cm^{2}}$

⠀⠀

⠀⠀⠀⠀$\sf{:\implies \dfrac{22}{7}×15×29.21\:cm^{2}}$

⠀⠀

⠀⠀⠀⠀$\sf{:\implies 1377.04\:cm^{2}}$

⠀⠀

Therefore,

Total surface area of the cone is 1377.04 cm²

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