The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its (i) curved surfaces area (ii) total surface area.

Answer

Curved surface area of a frustum is `628cm^2`, Total surface area of a frustum is `1356.48 cm^2`.

Explanation

The radii of ends of a frustum are 14 cm and 6 cm.
`:.r_1= 14" and "r_2=6 cm`
its height (h) = 6 cm
Let the slant height of the frustum be l.
`l=sqrt(h^2+(r_1-r_2)^2)`
`:. L=sqrt(6^2+(14-6)^2)`
`:.l=sqrt(36+8^2)`
`:.l=sqrt(36+64)`
`:.l=sqrt100`
`:.l=10 cm`
(i) Curved surface area fo a frustum `=pil(r_1+r_2)`
`=3.14xx10xx(14+6)`
`= 3.14xx10xx 20`
`= 628 cm^2`...(1)
(ii) Total surface area of a frustum
`=pil(r_1+r_2)+pir_1^2+pir_2^2`
`= 628 + pi(r_1^2+r_2^2)`
`=628+3.14(14^2+6^2)`
`=628+3.14(196+36)`
`=628+3.14xx232`
`=628+ 728.48`
`=1356.48 cm^2`