Question

The curved surface area of cone is 220cm² radius is 7cm what is its height
pls answer​

Answer 1

Answer:

10 cm

Step-by-step explanation:

Radius of cone (r) = 7 cm

Curved surface area of cone = 220 sq cm

=> πrl = 220

=> 22/7 × 7 ×l = 220

=> 22× l. =220

=> l. = 220/22 = 10 cm

Therefore slant height of the cone will be 10 cm

I hope this will help you, thank you

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that

Slant height of cone = l cm

Height of cone = h cm

Given that,

Radius of cone, r = 7 cm

Curved Surface Area of cone = 220 cm²

We know, Curved Surface Area of cone of slant height l and radius r is given by

$\boxed{ \rm{ \:CSA_{(Cone)} \: = \: \pi \: r \: l \: \: }}$

So, on substituting the values, we get

$\ \: 220 = \dfrac{22}{7} \times 7 \times l$

$\: 220 = 22 \times l$

$\implies \:l \: = \: 10 \: cm$

Now, we know slant height l, height h and radius r are connected by the relationship

$\: {l}^{2} = {r}^{2} + {h}^{2}$

So, on substituting the values of l and h, we get

$\: {10}^{2} = {7}^{2} + {h}^{2}$

$\rm \: 100 = 49 + {h}^{2}$

$\rm \: 100 - 49 = {h}^{2}$

$\rm \: {h}^{2} = 51$

$\rm \: h = \sqrt{51}$

So,

$\rm\implies \:\boxed{ \rm{ \:h \: = \: \sqrt{51} = 7.14 \: cm \: \: }}$

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Note :-

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:7.14 \:\:}}}\\ {\underline{\sf{7}}}& {\sf{51.0000}} \\{\sf{}}& \underline{\sf{49 \: \: \: \: \: \: \: \: }} \\ {\underline{\sf{141}}}& {\sf{200 \: \: \: }} \\{\sf{}}& \underline{\sf{141 \: \: \: }} \\ {\underline{\sf{1424}}}& {\sf{ \: \: \:\:5900}} \\{\sf{}}& \underline{\sf{ \: \: \: \: 5696}} \\ {\underline{\sf{}}}& {\sf{ \: \: \: \: \: \: 204}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$