Question

the radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm find its capacity and total surface area​

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption

Radius of the upper = 'R'

Lower radius = 'r'

R = 33 cm also r = 27 cm

Slant height = 10 cm

${\boxed{\sf\:{Using\:Formula:-}}}$

Slant height of frustum

= √h² + (R - r)²

⇒ 10 = √h²+ (33 - 27)²

⇒ 10² = h² + 36

⇒ h² = 100 - 36

⇒ h² = 64

⇒ h = 8 cm

${\boxed{\sf\:{Using\:Formula:-}}}$

Capacity of the frustum

$\tt{\rightarrow\dfrac{\pi h}{3}\times{R^2+r^2+Rr}}$

$\tt{\rightarrow\dfrac{22}{7}\times\dfrac{8}{3}\times[{33^2+27^2+(33\times 27)]}}}$

$\tt{\rightarrow\dfrac{22}{7}\times\dfrac{8}{3}\times 2709}}$

$\tt{\rightarrow\dfrac{476784}{21}}$

= 22704 cm³

Total surface area of the frustum

= π{R² + r² + l(R + r)}

$\tt{\rightarrow\dfrac{22}{7}\times{33^2 + 27^2 + 10(33+27)}}$

$\tt{\rightarrow\dfrac{22}{7}\times{1089+729+600}}$

$\tt{\rightarrow\dfrac{22}{7}\times{2418}}$

$\tt{\rightarrow\dfrac{53196}{7}}$

= 7599.43 sq cm