The base radius of a cone is 30 cm and height is 40 cm. a) Find the base perimeter of the cone b) Find the curved surface area of the cone
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The base radius of a cone is 30 cm and height is 40 cm. a) Find the base perimeter of the cone b) Find the curved surface area of the cone
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[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
Now,
[tex]\rm \: Base\:perimeter \: of \: cone \: = \: 2 \: \pi \: r \\ [/tex]
[tex]\rm \: = \: 2 \times \dfrac{22}{7} \times 30 \\ [/tex]
[tex]\rm \: = \: \dfrac{1320}{7} \: \\ [/tex]
So,
[tex]\bf\implies \: Base\:perimeter \: of \: cone \: = \: \dfrac{1320}{7} \: cm \\ \\ [/tex]
Now, To find curved surface area of cone, we have to first find the slant height of cone.
We know, slant height (l) of a cone is given by
[tex]\rm \: {l}^{2} = {h}^{2} + {r}^{2} \\ [/tex]
[tex]\rm \: {l}^{2} = {40}^{2} + {30}^{2} \\ [/tex]
[tex]\rm \: {l}^{2} = 1600 + 900 \\ [/tex]
[tex]\rm \: {l}^{2} = 2500 \\ [/tex]
[tex]\rm \: {l}^{2} = {50}^{2} \\ [/tex]
[tex]\rm\implies \:l \: = \: 50 \: cm \\ [/tex]
Now, Curved Surface Area of cone of radius r and slant height l is given by
[tex]\rm \: CSA_{(Cone)} \\ [/tex]
[tex]\rm \: = \: \pi \: r \: l \\ [/tex]
[tex]\rm \: = \: \dfrac{22}{7} \times 30 \times 50 \\ [/tex]
[tex]\rm \: = \: \dfrac{33000}{7} \: {cm}^{2} \\ [/tex]
Hence,
[tex]\bf\implies \: CSA_{(Cone)}\: = \: \dfrac{33000}{7} \: {cm}^{2} \\ \\ [/tex]
[tex]\rule{190pt}{2pt} \\ [/tex]
Additional Information :-
[tex]\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}[/tex]