A land-shade has a height of 12cm and upper and lower diameters of 20cm and 10cm. What area of material is required to cover the curved surface of the land-shade?

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chandrachaks's profile pic

chandrachaks | Elementary School Teacher | (Level 1) Adjunct Educator

Posted on

Let R and r be the radius of upper and lower radii . Let h be the height.

Now, R= Upper diameter / 2= 20/2=10 cm.

again r = lower diameter / 2= 10/2=5 cm.

 and h=12 cm.

let s be the slant height of the land-shade then

solving this we get , s= 13 cm.

now, area of cloth needed is the lateral surface area of the land-shade= π(R+r)l

= 3.14*(10+5)13

= 612.3 sq.cm

Sources:
embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The area we are looking for is the surface area of a right circular frustum, excluding the areas of the circles.

The formula is `A=pi(R_1+R_2)s ` where A is the area we seek, R1 and R2 are the radii of the circles and s is the slant height.

The slant height is given by `s=sqrt((R_1-R_2)^2+h^2) ` where h is the height of the frustum. (This is the Pythagorean theorem with s as the hypotenuse. See picture in link.)

So ` A=pi(R_1+R_2)sqrt((R_1-R_2)^2+h^2) `

`R_1=5,R_2=10,h=12 `

`A=pi(5+10)sqrt(5^2+12^2) `

`A=pi(15)(13) `

`A=195pi~~612.61 `

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The area of material required is approximately 612.61 square cm.

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