Question

the surface area of a sphere is equal to the sum of the curved surface areas of two cylinders of length 12cm and 18cm having their radii is 3.5cm each. Find the surface area of the sphere.​

Answer 1

Step by step explanation

$4\pi {r}^{2} = 2\pi rh \: + 2\pi rh$

$4\pi \: r^{2} = 2\pi \times 3.5 \times 12 \: \: + 2\pi \times 3.5 \times 18$

$4\pi {r}^{2} = 2\pi(42 + 63)$

$4\pi {r}^{2} = 2\pi \times 105$

$\frac{4\pi {r}^{2} }{2\pi} = 105$

$2 {r }^{2} = 105$

${r}^{2} = \frac{105}{2}$

${r}^{2} = 52.5$

$r = \sqrt{52.5}$

$r = 7.2456cm$

$r = 7.25cm \: (approx)$

$Surface \: Area \: of \: Sphere = 4πr ^{2}$

$= 4 \times 3.14 \times 52.5$

$= 659.4 {cm}^{2}$

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