Question

24. The diameter of a cone is 10cm and height is 12cm. Calculate the total surface
area of the cone.​

Answer 1

Question:-

The diameter of a cone is 10cm and height is 12cm. Calculate the total surface

area of the cone.

Answer:-

Given: radius = 10 cm and height = 12 cm

R = radius of base, h = height of cone, and s = slant height:

$[s = \sqrt[]{r {}^{2} + h {}^{2} } ]$

•Total surface area: (T)

$T = π⋅r⋅(r+s)=π⋅r⋅(r + \sqrt[]{r {}^{2} + h {}^{2} } )$

$T = π⋅10⋅(10 + \sqrt[]{10 {}^{2} + 12 {}^{2} } )$

$= 804.8917254 \: sq \: cm \: or ≈ 80.49 \: sq \: m$

•Lateral surface area: (S) [base excluded]

$S = π⋅r⋅s=π⋅r⋅ \sqrt[]{r {}^{2} + h {}^{2} }$

$S = π⋅10⋅ \sqrt[]{10 {}^{2} + 12 {}^{2} } </p><p></p><p>$

$= 490.7324601 \: sq \: cm \: or ≈ \: 49.07 \: sq \: m</p><p></p><p>$