The sum of the radius of the base and the height of a solid cylinder is 74 metres. What is the volume if its total surface is 13024 sq. m?

25440 m³

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36960 m³

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41920 m³

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52720 m³

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None of these

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Solution

The correct option is B
36960 m³

(h + r) = 74 and 2 $π$ r (h+r) = 6512 $∴$ 2 $π$ r $\times$ 74 = 6512 or r = $(\frac{6512}{2 \times 74} \times \frac{7}{22}) = 14$ So, r = 14 m and h = 60 m. $∴$ Volume $(\frac{22}{7} \times 14 \times 14 \times 60)$ m $^{3}$ = 36960 m $^{3}$

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The sum of the radius of the base and the height of a solid cylinder is 74 metres. What is the volume if its total surface is 13024 sq. m?

The correct option is B 36960 m3 (h + r) = 74 and 2πr (h+r) = 6512 ∴2πr×74 = 6512 or r = (65122×74×722)=14 So, r = 14 m and h = 60 m. ∴Volume (227×14×14×60) m3= 36960 m3

The correct option is B
36960 m³

(h + r) = 74 and 2 $π$ r (h+r) = 6512 $∴$ 2 $π$ r $\times$ 74 = 6512 or r = $(\frac{6512}{2 \times 74} \times \frac{7}{22}) = 14$ So, r = 14 m and h = 60 m. $∴$ Volume $(\frac{22}{7} \times 14 \times 14 \times 60)$ m $^{3}$ = 36960 m $^{3}$