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Surface Areas and Volumes — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsSurface Areas and Volumes1 Mark
Question
Write ‘True’ or ‘False’ and justify your answer in the following: A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid $\pi\text{r}\Big[\sqrt{\text{r}^2+\text{h}^2}+3\text{r}+2\text{h}\Big].$
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Answer

False:Cone:
Radius = r
Height = h
Cylinder:
Radius = r
Height = h
Total surface area of the combined solid = Curved surface area of cone + Area of the base of cylinder

$=\pi\text{rl}+2\pi\text{rh}+\pi\text{r}^2=\pi\text{r}[\text{l}+2\text{h}+\text{r}]$
$\because\ \ \text{l}=\sqrt{\text{r}^2+\text{h}^2}$
$\therefore$ Total surface area of the combined solid
$=\pi\text{r}\Big[\sqrt{\text{r}^2+\text{h}^2}+2\text{h}+\text{r}\Big]$ which is not according to the given statement.
Hence, the given statement is false.

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