Question

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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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Answer 1

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

Step-by-step explanation:

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

using similarities:

`\sf (45 + h2)/(28) = (h2)/(7)`

`\sf 315 + 7h2 = 28h2`

`\sf 315 = 28h2-7h2`

`\sf 315 = 21h2`

`\sf 15 = h2`

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

solve for volume:

`\sf volume \ of \ cone \ = (1)/(3) \pi r^2 h`

`\sf volume \ of \ cone \ = (1)/(3) \pi (28)^2 (60)`

`\sf volume \ of \ cone \ = 15680\ *(22)/(7)`

`\sf volume \ of \ cone \ = 49280 \ cm^3`

First find the slant height using Pythagoras theorem -

`\sf l^2 = r^2 + h^2`

`\sf l =√( r^2 + h^2)`

`\sf l =√( (28)^2 + (60)^2)`

`\sf l =66.212 \ cm`

solve for curved surface area:

`\sf curved \ surface \ area = \pi rl`

`\sf curved \ surface \ area = \pi (28)(66.2)`


`\sf curved \ surface \ area =5826.64 \ cm^2`