Question

19 (a) A spherical tennis ball and a spherical beach ball have diameters in the ratio 1:3
The surface area of the beach ball is 153 cm².
Calculate the surface area of the tennis ball.​

Answer 1

Answer:

17cm²

Step-by-step explanation:

The diameters' ratio of a spherical tennis ball and a spherical beach ball is 1:3.

diameter d=2r

r=d/2.

so there radius' ratio

$\frac{ \frac{1}{2} }{ \frac{3}{2} } \\ \frac{1}{3}$

suppose the radius of tennis ball is Rt. then radius of beach ball is Rb.

Rt:Rb=1:3

We know that,

and the surface Area of a spherical object is

$4\pi {r}^{2}$

here, square of radius is directly proportional to surface area of a spherical object.

suppose the surface are of tennis ball is At and the surface area of beach ball is Ab.

At:Ab=(Rt:Rb)²

At:Ab=(1:3)²

At:Ab=1:9

surface area of beach ball is given and that is 153 cm²

then,

At:153=1:9

At=(1:9)*153

=153/9

=17 cm²