Question

The circumference of base of a conical tent is 44 cm. If the height of the tent is 24 cm, find the length of the canvas used in making the tent, if the width of the canvas is 2 cm.

Answer 1

Circumference of circle = 2$\bold{\pi}$r

Given in question that circumference of base of a conical tent is 44 m.

So,

→ 44 = 2$\pi$r

→ 44 = 2 × 22/7 × r

→ (44 × 7)/44 = r

→ r = 7 cm

Height of tent is 24 cm.

So,

Slant height (l) of conical tent = √(h² + r²)

→ l = √[(24)² + (7)²]

→ l = √(576 + 49)

→ l = √625

→ l = 25 cm

Now,

Area of rectangular canvas = Surface area of tent

→ l × b = $\pi$rl

→ l × 2 = 22/7 × 7 × 25

→ l × 2 = 22 × 25

→ l = 11 × 25

→ 275 cm

∴ Length of canvas used in making the tent is 275 cm.

Answer 2

Answer:

The circumference of base of a conical tent = 44 cm.

The height of a conical tent = 24.

$2\pi \: r \: = 44$

$2 \times \frac{22}{7} \times r \: = 44$

$r = 44 \times \frac{7}{22} ? \times \frac{1}{2}$

$r \: = \: 7 \: cm$

$curved \: surface \: area = r \: \times \pi$

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

${l}^{2} = {24}^{2} + {7}^{2}$

${l}^{2} = 25cm$

$curved \: surface \: area = \frac{22}{7} \times 7 \times 25$

$curved \: surface \: area \: = \: 550 \: {cm}^{2}$

$area \: of \: the \: canvas \: = \: curved \: surface \: area \: = lr\pi \: = l \: \times b$

$l \: = \sqrt{} {(24)}^{2} + {(7)}^{2}$

$l = \sqrt{(576 \: + \: 49)}$

$l \: = \sqrt{625}$

$l = 25cm$

$area \: of \: rectangular \: canvas \: = \: surface \: area \: of \: tent \:$

$= l \: \times b \: = \pi \: rl$

l × 2 = 22/7 × 7 × 25

l × 2 = 22 × 25

l = 11 × 25

$= l \: = \: 275 \: cm.$