Question

if x be the slant height of frustum of a cone p and q are the base radii find the ratio of TSA and CSA

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The ratio of TSA and CSA of frustum of cone is p² : - q²

Step-by-step explanation:

Slant height of frustum of a cone ($l_1$)   = x

Base radius  (R) = p

base radius (r) = q

Find the ratio of Total surface and Curved Surface area of frustum of cone

$\text { The total surface area of the frustum of the cone }=\pi \mathrm{l}_{1}(\mathrm{R}+\mathrm{r})+\pi \mathrm{R}^{2}+\pi \mathrm{r}^{2}$

Substitute the respective values in above formula

$\text { The total surface area of the frustum of the cone }=\pi \mathrm x (\mathrm{p}+\mathrm{q})+\pi \mathrm{p}^{2}+\pi \mathrm{q}^{2}$

$The curved surface area of the frustum of the cone =\pi(\mathrm{R}+\mathrm{r}) \mathrm{I}_{1}$

Substitute the respective values in above formula

$The curved surface area of the frustum \space of the cone =\pi(\mathrm{p}+\mathrm{q}) \mathrm{x}$

The ratio of total surface and curved surface area of frustum of a cone is given by

Total surface area : Curved Surface area

The term π x (p+q) can be cancelled  on both sides

$\pi \mathrm x (\mathrm{p}+\mathrm{q})+\pi \mathrm{p}^{2}+\pi \mathrm{q}^{2} : \pi(\mathrm{p}+\mathrm{q}) \mathrm{x}$

$\pi \mathrm{p}^{2}+\pi \mathrm{q}^{2} : 0$

$\pi \mathrm{p}^{2} : - \pi \mathrm{q}^{2}$

p² :  -q²

1 : -1

Therefore the ratio of Total surface and curved surface area of frustum of a cone is p² : - q², when the slant height is 'x' , and base radii are 'p' and 'q'

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