Question

20. If the radii of the ends of a buckets are 5cm and 15 cm and 24cm high, find its surface area. (Use pi =3.14) (set 2)

Answer 1

Formula is 2πrh+2πr(squared)
SA(5cm by 24 cm bucket)= 911.06
SA( 15cm by 24cm bucket)= 3675.66
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Answer 2

Given :-

• Radius of the top of bucket = 15 cm
• Radius of the bottom of bucket = 5 cm
• Height of the bucket = 24 cm.

To Find :-

• Surface area of the bucket.

Solution :-

• Here the bucket is in shape of a frustum.Let us find the slant height first!

$\sf\red{\: \: \: \: \: \: \: :\implies Slant\: Height= \sqrt{(R-r)^2+h^2}}$

$\: \: \: \: \: \: \: : \implies\sf Slant\: Height_{Bucket}= \sqrt{15-5)^2+(24)^2}$

$\: \: \: \: \: \: \: : \implies\sf Slant\: Height_{Bucket}= \sqrt{(10)^2+(24)^2}$

$\: \: \: \: \: \: \: : \implies\sf Slant\: Height_{Bucket}= \sqrt{100+576}$

$\: \: \: \: \: \: \: : \implies\sf Slant\: Height_{Bucket}= \sqrt{676}$

$\: \: \: \: \: \: \: : \implies{\boxed{\pink{\sf\ Slant\: Height_{Bucket}= 26 cm}}}$

$\therefore\:\underline{\textsf{Slant height of the bucket is \textbf{26 cm }}}$

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$\red{\: \: \: \: \: \: \: : \implies\sf\ S.A= π\times (R+r)\times l}$

$\: \: \: \: \: \: \: : \implies\sf\ S.A_{Bucket}= 3.14\times (15+5)\times 26$

$\: \: \: \: \: \: \: : \implies\sf\ S.A_{Bucket}=81.64\times 20$

$\: \: \: \: \: \: \: : \implies\sf\ S.A_{Bucket}= 1634.28$

$\: \: \: \: \: \: \: : \implies{\boxed{\pink{\sf\ Surface\ Area_{Bucket}= 1634.28 cm^2}}}$

$\therefore\:\underline{\textsf{Surface area of the bucket is \textbf{ 1634.28 cm²}}}$