Question

the radii of a circular ends of a bucket of height 24cm and 15 cm and 5 cm find the area of its curved surface area

Answer 1

$\underline {\red{\bold{Here\: is \: your \:solution}}}$

Given :-

Height of a bucket = 24cm (h)

Radius of circular ends of bucket 5cm and 15cm

r1 = 5cm
r2 = 15cm

Let
slant height of bucket be l

To find the area of its curved surface area:-

Now

$l = \sqrt{(r1 + r2) {}^{2} + h {}^{2} } \\ l = \sqrt{(15 {}^{2} - 5) {}^{2} + 24 {}^{2} } \\ l = \sqrt{100 + 576} \\ l = \sqrt{676} \\ l = 26cm \\ \\ \\ curved \: surface \: area = \\ \pi(r1 + r2)l + \pi \: r2 {}^{2} \\ = \pi (5 + 15)l + \pi \: \times 15 {}^{2} \\ = \pi(20)26 + 225\pi \\ = 520\pi + 225\pi \\ = 745\pi \\ = 745 \times 3.14 \\=2,339.3 cm^2$

Hence

$\underline {\red{\bold{The \:curved\: surface \:area}}}$
$\underline {\red{\bold{of \:bucket\: is \:2339.3\:cm^2}}}$

Answer 2

Solutions :-

Given :

Height of the bucket = h = 24 cm
Radius of top bucket = R = 15 cm
Radius of bottom bucket = r = 5 cm

Let the slant height be L

Find the slant height :-

We know that,
L = √ (h)² + ( R - r )²

A/q

=> ✓ ( 24)² + ( 15 - 5 )²
=> √576 + (10)²
=> √ 576 + 10
=> √676
=> 26 cm.

Find the Curved Surface area of bucket :-

Curved surface area = π(R+r)L+πR² square unit
= 22/7 (15 + 5)26 + 22/7 (15)² cm²
= (3.14 × 20 × 26) + (3.14 × 225) cm²
= 1632.8 + 706.5 cm²
= 2339.3 cm²


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Hence,
Curved surface area of bucket = 2339.3 cm²