find the lateral area, total area and volume of a frustum of the right circular cone if the slant height is 15 cm and the radii of the bases are 12 cm and 18 cm

Question

is there a difference in formula in case of right frustum of a cone and frustum of a right circular cone ? 

Answer 1

VOLUME:  The first step is to find the vertical height from the slant height.  The relationship is:

 

S² = h² + (R-r)²

S = slant height

h = vertical height (distance between bases)

R = radius of the larger base

r = radius of the smaller base

 

So 15² = h² + (18 - 12)²

225 = h² + 36

189 = h²

√189 = h

 

The formula for the volume is (πh/3)(R² + Rr + r²)

 

So that's (π√189/3) (18² + 12*18 + 12²) =

(π√189/3) (684) =

228π√189 cm³

 

LATERAL AREA:  The formula for the lateral area is

 

A_L = π (R + r)√((R - r)² + h²) =

π (18 + 12)√((18 - 12)² + (√189)²) =

30π √(36 + 189) =

30π √225 =

15 * 30π =

450π

 

TOTAL AREA:  Add the areas of the bases to the lateral area:

 

A_T = A_L + πR² + πr²

450π + π18² + π12² =

450π + 324π + 144π =

918π