Question

the radius and height of a cylinder are in the ratio 4:7.find the radius and height of the cylinder if it's volume is 1188cu cm. also find the total surface area.

Answer 1

radius and height are in the ratio 4:7
let radius, r = 4x
height, h = 7x

volume = πr²h
⇒ 1188 = π × (4x)² × 7x
⇒ 1188 = (22/7) ×16x² × 7x
⇒ 1188 = 22×16x² × x
⇒ 1188 = 352x³
⇒ x³ = 1188/352 = 27/8
⇒ x = ∛(27/8) = 3/2 = 1.5cm

radius = 4x = 4×1.5 = 6cm
height = 7x = 7×1.5 = 10.5 cm

TSA = 2πr(r+h)
        = 2×(22/7)×6(6+10.5)
        = 836.28 cm²

Answer 2

radius and height are in the ratio 4:7
 radius( r) = 4k
height( h )= 7k
volume(v)=[tex] \pi r^{2} h \\ = \frac{22}{7} *(4k) ^{2} *7k \\ \\ \frac{22}{7}*112k ^{3} \\ \\ volume=352 k^{3} \\ volume=1188 cm ^{3} \\ \\ 352 k^{3} =1188 \\ k ^{3} =1188/352=3.375 \\ k=1.5 \\
radus=4k=4*1.5=6 [/tex]
height = 7x = 7×1.5 = 10.5 cm

TSA = 2πrh+2πr²
        = 2*22/7*6*10.5+2*22/7*36
        = 836.28 cm²