Question

if the slant height and the base radius of a cone are 10 cm and 8 cm respectively, then find
(i) curved surface area and
(ii) total surface area. [take π = 3.14]
(iii) height
(iv) Volume​

Answer 1

Answer:

Total surface area: The total area occupied by the surface including the curved part and the base(s).

Curved surface area: The area occupied by the surface excluding the base(s) is known as curved surface area.

Volume: The space occupied by an object, which is measured in cubic units.

A right circular cone is a geometric figure having a circular base. Consider a right circular cone having ‘r’ as the base area, ‘h’ as the height of a cone and ‘l’ as a slant height. Then,

Total surface area = πr(r + l),

Curved surface area = πrl and

Volume = 1/3πr2h

Step-by-step explanation:

please see the attachment

Answer 2

${ \pmb{ \sf{Question : }}}$If the slant height and the base radius of a cone are 10 cm and 8 cm respectively, then find

(i) Curved surface area

(ii) Total surface area

(iii) Height

(iv) Volume⠀⠀

⠀⠀━━━━━━━━━━━━━━━━━━

$\pmb{ \sf {Diagram : }}$

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{r}}\put(9.5,10){\sf{h}}\end{picture}$⠀⠀

⠀⠀━━━━━━━━━━━━━━━━━━

$\pmb{ \sf { Formula \: to \: be \: used: }}$

$:\mapsto{\small{\underline{\boxed{\sf{CSA \: of \: cone =πrl }}}}}$

$: \mapsto{\small{\underline{\boxed{\sf{TSA \: of \: cone =πr(l + r) }}}}}$

$: \mapsto{\small{\underline{\boxed{\sf{ {l}^{2} = {r}^{2} + {h}^{2} }}}}}$

$: \mapsto{\small{\underline{\boxed{\sf{volume \: of \: cone = \frac{1}{3} π {r}^{2}h }}}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

$\pmb{ \sf { Solution: }}$

$\bigstar \: \sf{CSA = \pi × 10 × 8} \\\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \purple{251.2 cm^2}}$

$\bigstar \: \sf{TSA = \pi × 8(10 + 8)} \\\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \purple{452.16 cm^2}}$

$\bigstar \: \sf{l^2= h^2 + r^2} \\ \sf{ {10}^{2} = h^2 + {8}^{2}} \\ \sf{{10}^{2} - {8}^{2} = {h}^{2} } \\ \sf{{100 - 64 = h^2 }} \\ \sf{{36 = h^2 }} \\ \sf{{ \sqrt{36} = h }} \\ \sf \purple{{6 cm = h }}$

$\bigstar \: \sf{volume = \frac{1}{3} \times \pi \times 8 \times 8 \times 6 } \\ \sf \purple{ = 401.92 \:cm^{3} }$

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