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Here's a question :-

1) The radii of the ends of a frustum of a cone 45cm high are 28cm and 7cm ( see figure ) . Find it's volume , the curved surface area ( Take π = 22/7 ) .

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Hᴇʟʟᴏ Bʀᴀɪɴʟɪᴀɴs Nᴇᴇᴅ Hᴇʟᴘ Heres A Question 1 The Radii Of The Ends Of A Frustum Of A Cone 45cm High Are 28cm And 7cm See Figure Find Its Volume The Curved Surf class=

Sagot :

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Answer:

volume: 49280 cm³  and   curved S.A = 5826.64 cm²

Explanation:

  • height of smaller cone: h₂
  • radius of smaller cone: 7
  • height of bigger cone: 45 + h₂
  • radius of bigger cone: 28

using similarities:

[tex]\sf \frac{45 + h2}{28} = \frac{h2}{7}[/tex]

[tex]\sf 315 + 7h2 = 28h2[/tex]

[tex]\sf 315 = 28h2-7h2[/tex]

[tex]\sf 315 = 21h2[/tex]

[tex]\sf 15 = h2[/tex]

total height of the cone: 45 + 15 = 60 cm

solve for volume:

[tex]\sf volume \ of \ cone \ = \frac{1}{3} \pi r^2 h[/tex]

[tex]\sf volume \ of \ cone \ = \frac{1}{3} \pi (28)^2 (60)[/tex]

[tex]\sf volume \ of \ cone \ = 15680\ *\frac{22}{7}[/tex]

[tex]\sf volume \ of \ cone \ = 49280 \ cm^3[/tex]

First find the slant height using Pythagoras theorem -

[tex]\sf l^2 = r^2 + h^2[/tex]

[tex]\sf l =\sqrt{ r^2 + h^2}[/tex]

[tex]\sf l =\sqrt{ (28)^2 + (60)^2}[/tex]

[tex]\sf l =66.212 \ cm[/tex]

solve for curved surface area:

[tex]\sf curved \ surface \ area = \pi rl[/tex]

[tex]\sf curved \ surface \ area = \pi (28)(66.2)[/tex]

[tex]\sf curved \ surface \ area =5826.64 \ cm^2[/tex]

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