If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high, then its surface area is

Question:

If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high, then its surface area is
(a) 1815.3 cm2
(b) 1711.3 cm2
(c) 2025.3cm2
(d) 2360 cm2

 

Solution:

(b) 1711.3 cm2
Let R and r be the radii of the top and base of the bucket, respectively, and let h and l be its height and slant height.

Then, 

$R=15 \mathrm{~cm}, r=5 \mathrm{~cm}, h=24 \mathrm{~cm}$

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

$=\sqrt{(24)^{2}+(15-5)^{2}}$

$=\sqrt{576+100}$

$=\sqrt{676}$

$=26 \mathrm{~cm}$

Surface area of the bucket $=\pi\left[r^{2}+l(R+r)\right]$

$=3.14 \times\left(5^{2}+26(15+5)\right)$

$=(3.14 \times(26 \times 20+25)) \mathrm{cm}^{2}$

$=1711.3 \mathrm{~cm}^{2}$

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