Question

5.The slant height of a bucket is 26 cm. The diameter of upper and lower circular ends are 36 cm and 16 cm. then height of bucket is:​

Answer 1

Given:

• Slant height of bucket = 26 cm
• Upper diameter of bucket = 36 cm
• Lower diameter of bucket = 16 cm

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To find:

• Height of bucket ?

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Solution:

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☯ Let height of bucket be h cm.

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Here,

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• Upper diameter of bucket = 36 cm

∴ Upper radius of bucket, R = 36/2 = 18 cm

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And,

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• Lower diameter of bucket = 16 cm

∴ Lower radius of bucket, r = 16/2 = 8 cm

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We know that,

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$\star\;{\boxed{\sf{\purple{l^2 = h^2 + (R - r)^2}}}}$

Putting values,

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$:\implies\sf 26^2 = h^2 + (18 - 8)^2$

$:\implies\sf 676 = h^2 + (10)^2$

$:\implies\sf 676 = h^2 + 100$

$:\implies\sf h^2 = 676 - 100$

$:\implies\sf h^2 = 576$

$:\implies\sf \sqrt{h^2} = \sqrt{576}$

$:\implies{\boxed{\frak{\pink{h = 24\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\;height\;of\; bucket\;is\;{\textsf{ \textbf{24\;cm}}}.}}}$

Answer 2

Answer:

Given :-

• The slant height of a bucket is 26 cm.
• The diameter of upper and lower circular ends are 36 cm and 16 cm respectively.

To Find :-

• What is the height of the bucket.

Formula Used :-

$\boxed{\bold{\large{l\: =\: \sqrt{{h}^{2} +\: {(R - r)}^{2}}}}}$

Solution :-

Given :-

Let, the height of the bucket be h

◪ Slant height (l) = 26 cm

◪ Upper diameter = 36 cm

◪ Upper radius (R) = 18 cm

◪ Lower diameter = 16 cm

◪ Lower radius (r) = 8 cm

According to the question by using the formula we get,

⇒ 26 = $\sqrt{{h}^{2} +\: {(18 - 8)}^{2}}$

⇒ 26 = $\sqrt{{h^2} + {10^2}}$

⇒ (26)² - (10)² = h²

⇒ 676 - 100 = h²

⇒ h = $\sqrt{576}$

➠ h = 24 cm

$\therefore$ The height of the bucket is 24 cm .

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