Question

A girl wishes to prepare birthday caps in the
form of right circular cones for her birthday
party, using a sheet of paper whose area is
5720 cm², how many caps can be made with
radius 5 cm and height 12 cm.
​

Answer 1

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Given:

A girl want to make right circular cones cap using a sheet of paper whose area is 5720 cm²

Right circular cone,

Radius = 5 cm

Height = 12 cm

To find:

Number of caps formed from sheet of paper of area 5720 cm² = ?

Solution:

For finding area of birthday cone cap we will use curved surface area formula of cone.

$\\ \\ Cuved \: \: surface \: \: area \: \: of \: \: cone \\ \\ = \pi \: rl \\ \\ where \: r = radius \\ \\ l = slant \: height$

For finding curved surface we have to find slant height

$\\ \\ slant \: height (l)\: = \sqrt{r {}^{2} + h{}^{2} } \\ \\ where \: r = base \: radius \: of \: cone \\ \\ h = height \: of \: cone$

$\\ l = \sqrt{(5) {}^{2} + (12) {}^{2} } \\ \\ = \sqrt{25 + 144} \\ \\ = \sqrt{169} \\ \\ = 13 \: cm$

$\\ curved \: surface \: area \: = \pi \: rl \\ \\ = \pi \times 5 \times 13 \\ \\ = 65\pi \: cm {}^{2} \\ \\ we \: will \: solve \: for \: \pi \: later \: to \: solve \: \\ \\ easily$

65π cm² required for 1 cone cap

5720 cm² required for 5720×1/65 π caps

By solving

$\\ \\ = \dfrac{5720 \times 1}{65\pi} \\ \\ = \dfrac{5720 \times 1}{ 65 \times \frac{22}{7} } \\ \\ = \dfrac{5720 \times 7}{65 \times 22}$

$\\ \\ = \dfrac{40040}{1430} \\ \\ = 28$

Required answer:

Therefore, 28 caps can be made from 5720 cm² area sheet paper

Knowledge booster:

# We used curved surface area formula because birthday caps are curved and not totally covered

# Example: If 1 cap required 5 cm² area sheet paper so for making 10 caps how many area sheet paper required?

----> 1 cap = 5 cm²

10 caps = 10×5/1 = 50 cm² area sheet paper

# Take care to use correct formula of total surface area of cone and curved surface area of cone. Solve more such questions to get good hold on it

Answer 2

Step-by-step explanation:

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