The difference between the height and the radius of a solid cylinder is 23 cm. The total surface area of the cylinder is 1628 cm22,The height and the radius of the cylinder, respectively, are (π=22/7) :

The difference between the height and the radius of a solid cylinder is 23 cm. The total surface area of the cylinder is 1628 cm22,The height and the radius of the cylinder, respectively, are π= $\frac {22}{7}$ :

Options
a) 33 cm , 10 cm
b) 30 cm , 7 cm
c) 32 cm , 09 cm
d) 28 cm , 5 cm

Solution

As per question
Difference between the height (h) and the radius (r) of a solid cylinder is 23 cm
h – r = 23
h = 23 + r

Surface area of the cylinder= 2π(rh + r²) = 1628
Put value of h in formula
2π (r (23 + r) + r² = 1628
$2 \times \frac {22}{7}$ (23r + r²+ r²) = 1628
23r + 2r² = $\frac {1628 \times 7}{22 \times 2}$ = 259
2r² + 23r = 259
2r² + 23r – 259 = 0
2r² + (37 – 14)r – 259 = 0
2r² – 14 + 37r – 259 = 0
2r (r – 7) + 37 (r – 7) = 0
(r – 7) (2r + 37) = 0
r – 7 , r = -37/2
r = 7 , r = -37/2

Radius(r) = 7
Put the value of r
h – r = 23
h – 7 = 23
height = 23 + 7 = 30

The difference between the height and the radius of a solid cylinder is 23 cm. The total surface area of the cylinder is 1628 cm22,The height and the radius of the cylinder, respectively, are π= :

Solution

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The difference between the height and the radius of a solid cylinder is 23 cm. The total surface area of the cylinder is 1628 cm22,The height and the radius of the cylinder, respectively, are π= $\frac {22}{7}$ :