Question

please give me answer​

Answer 1

Question:

The total surface area of a cone of radius r / 2 and height 2h is:

i) $\displaystyle{\sf\:2\:\pi\:r\:(\:h\:+\:r\:)}$

ii) $\displaystyle{\sf\:\pi\:r\:\left(\:h\:+\:\dfrac{r}{4}\:\right)}$

iii) $\displaystyle{\sf\:\pi\:r\:(\:h\:+\:r\:)}$

iv) $\displaystyle{\sf\:2\:\pi\:r\:h}$

Answer:

The total surface area of the cone would be

$\displaystyle{\pmb{\sf\:Option\:ii)}\sf\:\pi\:r\:\left(\:h\:+\:\dfrac{r}{4}\:\right)}$

Step-by-step-explanation:

We have given that,

• Radius of cone ( R ) = r / 2

• Slant height of cone ( l ) = 2h

We know that,

$\displaystyle{\boxed{\pink{\sf\:Total\:surface\:area\:of\:cone\:=\:\pi\:R\:(\:R\:+\:l\:)\:}}}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\pi\:.\:\dfrac{r}{2}\:\left(\:\dfrac{r}{2}\:+\:2h\:\right)}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\dfrac{\pi\:r}{2}\:\left(\:\dfrac{r\:+\:4h}{2}\:\right)}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\dfrac{\pi\:r\:(\:r\:+\:4h\:)}{2\:\times\:2}}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\dfrac{\pi\:r\:(\:r\:+\:4h\:)}{4}}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\pi\:r\:\left(\:\dfrac{4h\:+\:r}{4}\:\right)}$

$\displaystyle{\implies\sf\:TSA_{cone}\:=\:\pi\:r\:\left(\:\dfrac{\cancel{4}\:h}{\cancel{4}}\:+\:\dfrac{r}{4}\:\right)}$

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:TSA_{cone}\:=\:\pi\:r\:\left(\:h\:+\:\dfrac{r}{4}\:\right)\:}}}}$

∴ The total surface area of the cone would be

$\displaystyle{\boxed{\red{\sf\:\pi\:r\:\left(\:h\:+\:\dfrac{r}{4}\:\right)}}}$

Answer 2

Answer :

$\displaystyle{\sf\:Option\:ii)}\sf\:{\pi\:r\:\left(\:h\:+\:\dfrac{r}{4}\:\right)\:\:}$

Step-by-step-explanation :

Given that -

⭑Radius of cone (R) = r/2

⭑Slant height of cone (l) = 2h

We know that -

$\displaystyle{\boxed{\sf\:Total\:surface\:area\:of\:cone\:=\:\pi\:R\:(\:R\:+\:l\:)\:}}$

$\displaystyle{\sf\:=\:\pi\:.\:\dfrac{r}{2}\:\left(\:\dfrac{r}{2}\:+\:2h\:\right)}$

$\displaystyle{\sf\:=\:\dfrac{\pi\:r}{2}\:\left(\:\dfrac{r\:+\:4h}{2}\:\right)}$

$\displaystyle{\sf\:=\:\dfrac{\pi\:r\:(\:r\:+\:4h\:)}{2\:\times\:2}}$

$\displaystyle{\sf\:=\:\dfrac{\pi\:r\:(\:r\:+\:4h\:)}{4}}$

$\displaystyle{\sf\:=\:\pi\:r\:\left(\:\dfrac{4h\:+\:r}{4}\:\right)}$

$\displaystyle{\sf\:=\:\pi\:r\:\left(\:\dfrac{\cancel{4}\:h}{\cancel{4}}\:+\:\dfrac{r}{4}\:\right)}$

$\displaystyle{\underline{\boxed{\sf\:=\:\pi\:r\:\left(\:h\:+\:\dfrac{r}{4}\:\right)\:}}}$

∴ The total surface area of the cone would be

$\displaystyle{\boxed{\red{\sf\:\pi\:r\:\left(\:h\:+\:\dfrac{r}{4}\:\right)}}}$