Question

The total surface area of a cylinder is 264 m square.find its volume if its height is 5 more than its radius.

Answer 1

Answer:

327. 25 cubic meter

Step-by-step explanation:

Concept:

Total surface area of cylinder

= $2\pi\:r(h+r)$ square units

Volume of the cylinder =$\pi\:r^2\:h$ cubic units

Given:

h = r + 5

Total surface of the cylinder = 264 sq. m

$2\pi\:r(h+r)=264\\\\2\pi\:r(r+5+r)=264\\\\\pi\:r(2r+5)=132\\\\\frac{22}{7}r(2r+5)=132\\\\r(2r+5)=132(\frac{7}{22})\\\\2r^2+5r=6(7)\\\\2r^2+5r-42=0$

(r+6)(2r-7)=0

r = - 6, 7/2

r = -6, 3.5

But r cannot be negative.

r = 3.5 m

h = r + 5 = 3.5 + 5 = 8.5 m

Volume of the cylinder

$=\pi\:r^2\:h\\\\=(\frac{22}{7})(3.5)^2(8.5)\\\\=(\frac{22}{7})(3.5)(3.5)(8.5)$

= (22)(3.5)(0.5)(8.5)

=(11)(3.5)(8.5)

=(38.5)(8.5)

=327.25 m³

Answer 2

it is given that,

total surface of cylinder = 264 m²

height of cylinder = 5m + radius of cylinder.

Let height of cylinder is h

and radius of cylinder is r.

so, h = r + 5 .........(1)

then, total surface area = 264 m²

2πr² + 2πrh = 264 m²

from equation (1),

2πr² + 2πr(r + 5) = 264 m²

or, 2πr² + 2πr² + 10πr = 264 m²

or, 4πr² + 10πr = 264 m²

or, π(4r² + 10r) = 264 m²

or, 4r² + 10r = 264/π = 264 × 7/22

or, 4r² + 10r = 84

or, 4r² + 10r - 84 = 0

or, 2r² + 5r - 42 = 0

or, 2r² + 12r - 7r - 42 = 0

or, 2r(r + 6) - 7(r + 6) = 0

or, (2r - 7)(r + 6) = 0

hence, r = 7/2 and -6 but radius can't be negative so, r ≠ -6

hence, r = 7/2 or 3.5m

and h = r + 5 = 3.5 + 5 = 8.5m

now, volume of cylinder = πr²h

= 22/7 × 7/2 × 7/2 × 8.5

= 11 × 7/2 × 17/2

= (77 × 17)/4

= 327.25 m²