Question

Circular sheet of paper of radius 20 cm a sector of 30% area is removed and the remaining part is used to make up for a conical surface find the approximate volume of the conical surface in cubic cm and cube root of 51 equal to 7

Answer 1

Answer:

paper of radius 20

cm, a sector of 30%

area is removed and

the remaining part is

used to

make a

conical surface. Find

the approximate

volume of the

conical surface in

cubic cm ( Assume

V51 = 7)

Step-by-step explanation:

plzzlike

Answer 2

Answer:

The approximate volume of the conical surface is 2874.6 $cm^3$.

Step-by-step explanation:

The radius of the circular sheet, r = 20 cm

Area of circular sheet = $\pi r^2$

                                    = $\frac{22}{7}\cdot 20^2$

                                    = 1257.14 $cm^2$ (approx.)

Since a sector of 30% area is removed.

Area removed = 30% of 1257.14

                        = $\frac{30}{100}\cdot 1257.14$

                        = 377.14 $cm^2$ (approx.)

Remaining area of circular sheet = 1257.14 - 377.14

                                                        = 880 $cm^2$

According to the question,

880 $cm^2$ area of sheet is converted into conical surface.

⇒ 880 $cm^2$ = curved surface area of cone

⇒ 880 = $\pi Rl$, where $R$ = radius of cone and $l$ = slant height

Since radius of circular sheet = slant height of cone.

⇒ 880 = $\frac{22}{7}\cdot R \cdot20$ (Since $l$ = 20 cm)

⇒ $R=\frac{880 \cdot 7}{22\cdot 20}$

⇒ $R=14$ cm

Hence, radius of cone, R = 14 cm

Also,

Height of cone, h = $\sqrt{l^2-R^2}$

                             = $\sqrt{20^2-14^2}$

                             = $\sqrt{400-196}$

                             = $\sqrt{204}$

                             = $2\sqrt{51}$

                             = $14$ cm (Given: $\sqrt{51}=7$)

So, the volume of the cone = $\frac{1}{3} \pi R^2h$

                                 = $\frac{1}{3} \cdot\frac{22}{7} \cdot 14^2 \cdot14$

                                 = 2874.6 $cm^3$ (approx.)

Therefore, the approximate volume is 2874.6 $cm^3$.

SPJ3