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  • A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308·8 cm3. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet u

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308·8 cm3. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use \pi = 3·14)

 

 
 
 
 
 

Answers (1)

Volume of the frustum = 12308.8 cm3

                    \\r_1 = 20 \text{cm}\\r_2 = 12 \text{cm}

So,    

\begin{align*} \frac{1}{3}\pi h (r_1^2 + r_2^2 + r_1\cdot r_2)& =12308.8 \\\frac{1}{3}\times 3.14\times h (20^2 + 12^2 + 20\times 12) & = 12308.8\\ h &= \frac{12308.8\times 3}{78 4\times 3.14} \\ h & = 15 \ cm \end{align*}

The slant height of the basket,

 l = \sqrt{15^2 + {20-12}^2} = 17 \text{ cm}

\begin{align*}\text{Area of metal sheet used } & = \pi l(r_1+ r_2) + \pi r_2^2 \\ & = 3.14\left[17\times 32 + 12^2 \right ] \\ & = 2160.32 \ \text{cm}^2 \end{align*}

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Safeer PP

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