(a)
In the diagram, ABCD is a rectangular garden (3n – 1)m long and (2n + 1)m wide. A wire mesh 135m long is used to mark its boundary and to divide it into 8 equal plots. Find the value of n.
(b) A cylinder with base radius 14 cm has the same volume as a cube of side 22 cm. Calculate the ratio of the total surface area of the cylinder to that of the cube. [Take (pi = frac{22}{7})]
Explanation
(a) (3(3n – 1) + 5(2n + 1) = 135)
(9n – 3 + 10n + 5 = 135)
(19n + 2 = 135)
(19n = 135 – 2 = 133)
(n = frac{133}{19} = 7)
(b) Radius of a cylinder = 14 cm
side of a cube = 22 cm
(therefore frac{22}{7} times 14 times 14 times h = 22 times 22 times 22)
(44 times 14 times h = 22 times 22 times 22)
(h = frac{22 times 22 times 22}{44 times 14})
= (frac{121}{7} cm)
TSA of a cylinder = (2pi r (r + h) = 2 times frac{22}{7} times 14 (14 + frac{121}{7}))
= (88(frac{98 + 121}{7}) = frac{88 times 219}{7})
= (frac{19272}{7} cm^{2})
TSA of a cube = (6s^{2})
= (6 times 22 times 22)
= (2904 cm^{2})
Ratio = (frac{19272}{7} : 2904)
= (73 : 77)