Question

A CONE OF RADIUS 3 CM AND THE HEIGHT OF 4 CM, WHEN ITS SURFACE IS DEVELOPED FORMS A SECTOR. WHAT IS THE VALUE OF THE INCLUDED ANGLE OF THE SECTOR? Select one: a. 1129 b. 120° c. 205 d. 216​

Answer 1

Answer: 216°

Step-by-step explanation:

• Given,r=3 cm and h=4 cm

• Let l be the slant height of the cone. Then,

        $l^{2}=3^{2}+4^{2}$

    ⇒$l^{2}$= 9+16

    ⇒$l=\sqrt{25}$

     ∴ l = 5cm

• Area of the curved surface = πrl

                                                        = $\pi *3*5$

                                                        = $15\pi\ cm^{2}$

• Area of the sector=θ/360° $(\pi r^{2} )$
• According to question, θ/360° $(\pi r^{2} )$=$15\pi\ cm^{2}$  

                                           ⇒ θ=$\frac{15*360}{25}$       [∵ slant height=radius]

                                           ⇒ θ=3×72

                                          ∴  θ=216°

• Hence,the angle of sector is 216°.