Question
A bucket is in the from of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.
Answer: Option A
Volume of bucket :
= 28.490 litres
= (28.490 ×1000) cm3
= 28490 cm3
Let the height of the bucket be h cm
We have : r = 21 cm. and R = 28 cm
$$\therefore \frac{\pi }{3}h\left[ {{{\left( {28} \right)}^2} + {{\left( {21} \right)}^2} + 28 \times 21} \right]$$ $$ = 28490$$
$$ \Rightarrow h\left( {784 + 441 + 588} \right) = $$ $$\frac{{28490 \times 21}}{{22}}$$
$$\eqalign{
& \Rightarrow 1813h = 27195 \cr
& \Rightarrow h = \frac{{27195}}{{1813}} \cr
& \Rightarrow h = 15\,cm \cr} $$
Was this answer helpful ?
Volume of bucket :
= 28.490 litres
= (28.490 ×1000) cm3
= 28490 cm3
Let the height of the bucket be h cm
We have : r = 21 cm. and R = 28 cm
$$\therefore \frac{\pi }{3}h\left[ {{{\left( {28} \right)}^2} + {{\left( {21} \right)}^2} + 28 \times 21} \right]$$ $$ = 28490$$
$$ \Rightarrow h\left( {784 + 441 + 588} \right) = $$ $$\frac{{28490 \times 21}}{{22}}$$
$$\eqalign{
& \Rightarrow 1813h = 27195 \cr
& \Rightarrow h = \frac{{27195}}{{1813}} \cr
& \Rightarrow h = 15\,cm \cr} $$
Was this answer helpful ?
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