Question

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.​

Answer 1

Question :-

• Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

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${\large{\frak{\pmb{\underline{We\:have,}}}}}$

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$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ\: Radius\:of\:cone,\:r = 8\:cm$

$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\succ\: Height \:of\:cone,\:h = 15\:cm$

$\sf\:\:\:\:\:\:\succ\: Surface \:area \:of\: the \:shape \:=\:?$

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${\Large{\underline{\tt Now}}},$

$\bf\Large\:{\diamond}\:{\bold { \underline{\small{\:Surface\:area\:of\:shape\:so\:formed}}}}$

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$\:\:=\:$$\:\:\Bigg[$$\tt\small CSA \\\ \sf\small of\: first\:cone$ $\Bigg]$ + $\Bigg[$$\tt \small CSA \\\ \sf\small of\: second\:cone$ $\Bigg]$

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$\tt\:\:\:\:\:\:\:\:\:\:\:\:=\:2•Surface\:area\:of\:cone$

$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:|Since,\:both\:cones\:$$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:are\:identical|\:$

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$\sf\:\:\:\:\:\:\:\:\:=\:2×\pi r l=2×\pi×r×\bf\sf \displaystyle\sqrt{r²+h²}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:2×\bf\dfrac{22}{7} ×8\bf\sf \displaystyle\sqrt{(8)²+(15)²}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\bf\dfrac{2×22×8×\bf\sf \displaystyle\sqrt{64+225}}{7}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\bf\dfrac{44×8×\bf\sf \displaystyle\sqrt{289}}{7}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\bf\dfrac{44×8×17}{7}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\bf\dfrac{5984}{7}\:=\:854.85\:cm^²$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\boxed{\sf{=\frak{\red{855\:cm^{2}\:(approx)}}}}}$

Answer 2

After joining, the surface area vill con of lateral surface areas of two cones. ist

cm

r = 8cm

h = 15cm

|= v8? + 152 = v64+225 = 289 = 17cm

Surface area = 2xrl = 2x3.14x8x17 = 854