Question

the perimeter of the base of a cone is 44 cm and the slant height is 25 cm find the volume and the curved surface of the cone

Answer 1

Perimeter of the base of a cone = 44.

2πr = 44

2 × 22/7 × r = 44

r = ( 44 × 7 ) / 44

r = 7 cm.

Radius of cone ( r ) = 7 cm.

Slant height ( L ) = 25 cm.

Height ( H ) = ?

We know that,

Slant height of cone = ✓( Radius)² + (Height)²

(Slant height)² = Radius² + Height²

Height² = √(Slant height)² - (Radius)²

Height² = ✓(25)² - (7)²

Height² = 576

Height = √576 = 24 cm.

Height of cone ( H ) = 24 cm.

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Volume of cone = 1/3 πr² H

=> 1/3 × 22/7 × 7 × 7 × 24

=> (22 × 7 × 8 ) cm³.

=> 1232 cm³.

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Curved surface area of cone = πrL

=> 22/7 × 7 × 25

=> ( 22 × 25 ) cm².

=> 550 cm².

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Answer 2

$</p><p>{{\text{Let }}r{\text{ be the radius of base, }}h\,{\text{be the vertical height and }}l\, {\text{be the slant height of the right circular cone}}{\text{. }}\,} \\ </p><p>{{\text{Let }}r{\text{ be the radius of base, }}h\,{\text{be the vertical height and }}l\,{\text{be the slant height of the right circular cone}}{\text{. }}\,} \\ </p><p>\Rightarrow \,2\pi r\, = \,{\text{44 cm}} \hfill \\</p><p>\Rightarrow \,2 \times \frac{{22}}{7} \times r\, = \,{\text{44 cm}} \hfill \\ \Rightarrow \,r\, = \,\frac{{{\text{44}} \times 7}}{{2 \times 22}}{\text{ cm = 7 cm}} \hfill \\</p><p> \because \,{r^2} + {h^2} = {l^2} \hfill \\</p><p> {\text{Vertical height }}h\,{\text{of the cone }} \hfill \\</p><p> {\text{ = }}\sqrt {{l^2} - {r^2}} \, \hfill \\</p><p> {\text{ = }}\sqrt {{{25}^2} - {7^2}} \hfill \\</p><p>{\text{ = }}\sqrt {576} \, \hfill \\</p><p>therefore h = \,24\,{\text{cm}} \hfill \\</p><p> {\text{Volume}}\,{\text{of the cone }} \hfill \\</p><p> {\text{ = }}\frac{1}{3}\pi {r^2}h \hfill \\</p><p> = \frac{1}{3} \times \frac{{22}}{7} \times {7^2} \times 24 \hfill \\</p><p> = 22 \times 7 \times 8\, \hfill \\</p><p>= 1232\,{\text{c}}{{\text{m}}^3} \hfill \\</p><p> {\text{Curved surface}}\,{\text{of the cone }} \hfill \\</p><p> {\text{ = }}\pi rl \hfill \\</p><p> = \frac{{22}}{7} \times 7 \times 25 \hfill \\</p><p> = 22 \times 25\, \hfill \\</p><p>= 550\,{\text{c}}{{\text{m}}^2}\,\, \hfill \\ </p><p>$