Question

Anyone solve 22 number question

Answer 1

answer is 1386

Did you get the answer

Answer 2

The volume of solid figure is 1386 cm³

Step-by-step explanation:

• Given total height of solid = 20 cm

        Slant height of cone (L) =$\sqrt{218 }\ cm$

        Let radius of hemisphere and cone = R

        Height of solid cone (H) = 20 - R

• By using Pythagoras in cone

        $\mathbf{L^{2}=R^{2}+H^{2}}$

        $\mathbf{218=R^{2}+(20-R)^{2}}$

        218 = R² +400 +R² - 40 R

        2 R²- 40 R+400-218 = 0

        2 R²- 40 R+ 182 = 0

• On dividing all term by 2 in above equation, we get

        R²- 20 R+91 = 0

• Above equation can solve by middle term splitting method

        R²- 7 R -13 R+91 = 0

        R(R - 7) -13 (R - 7) =0

        (R -7) (R-13) = 0

• So solution of equation is

• R =13 ( Which is not acceptable because it is not multiple of 7)

        R = 7 cm (This is radius of hemisphere and cone)

• Then height of cone (H) = 20 - 7 = 13 cm

• Volume of solid = Volume of hemisphere + Volume of cone

        $\mathbf{Volume\ of\ solid=\frac{2}{3}\times \pi\times R^{3}+\frac{1}{3}\times \pi\times R^{2}\times H }$

         On putting respective value in above equation, we get

         $\mathbf{Volume\ of\ solid=\frac{2}{3}\times \pi\times 7^{3}+\frac{1}{3}\times \pi\times 7^{2}\times 13 }$

         $\mathbf{Volume\ of\ solid=\frac{\pi\times 7^{2} }{3}\left ( 2\times 7+13 \right ) }$

         $\mathbf{Volume\ of\ solid=\frac{\pi\times 7^{2} \times 27}{3} }$

         $\mathbf{Volume\ of\ solid=\frac{22\times 7^{2} \times 27}{7\times 3} }$

          On solving

          Volume of solid = 1386 cm³