17. Consider a sphere with a radius of 12 units. 17a Calculate the exact surface area of the sphere. Surface area $$ =576 \pi $$ square units 170. If the radius of the sphere is halved, find the new exact surface area. New surface area $$ = $$ $$ \square $$ Enter your next step here square units $$ \pm \text { () } \underset{x=}{x y} \quad a^{b} \quad \frac{a}{b} $$ TBC Submit step View next step

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UpStudy AI · Accepted Answer

1. The surface area $$ S $$ of a sphere with radius $$ r $$ is given by  
   $$
   S = 4\pi r^2.
   $$

2. For the original sphere with $$ r = 12 $$, we have  
   $$
   S = 4\pi (12)^2 = 4\pi \times 144 = 576\pi \text{ square units}.
   $$

3. If the radius is halved, the new radius is  
   $$
   r' = \frac{12}{2} = 6.
   $$

4. The new surface area $$ S' $$ is then  
   $$
   S' = 4\pi (6)^2 = 4\pi \times 36 = 144\pi \text{ square units}.
   $$
The new surface area is $$ 144\pi $$ square units.

Consider a sphere with a radius of 12 units.

17a Calculate the exact surface area of the sphere.
Surface area square units
170. If the radius of the sphere is halved, find the new exact surface area.

New surface area Enter your next step here square units

TBC
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Consider a sphere with a radius of 12 units. 17a Calculate the exact surface area of the sphere. Surface area square units 170. If the radius of the sphere is halved, find the new exact surface area. New surface area Enter your next step here square units TBC Submit step View next step