Question

Here are two spheres, with

radii 3 cm and 4.5 cm
respectively. The surface
area of the smaller sphere is
367 cm. What is the surface
area of the larger sphere?
4.6 cm
3 cm
A) 417 cm2
C) 817 cm2
B) 547 cm2
D) 121.57 cm2

Answer 1

The surface area of the larger sphere, with a radius of 4.5 cm, is calculated to be approximately 826 cm², closest to one of the provided options, 817 cm². The discrepancy is likely due to rounding in the answer choices.

Step-by-step explanation:

The surface area of a sphere is given by the formula A = 4πr², where 'A' stands for surface area and 'r' is the radius of the sphere. Since the surface area of the smaller sphere is given as 367 cm² and its radius is 3 cm, we can use this information to find the proportionality factor for the surface area of the larger sphere, which has a radius of 4.5 cm.

The ratio of the radii of the larger to smaller sphere is 4.5/3 or 1.5. Because surface area is proportional to the square of the radius, we square this ratio to find how much greater the surface area of the larger sphere is compared to the smaller one. Thus, the surface area of the larger sphere is 1.5² times the surface area of the smaller sphere, giving us 367 cm² * 2.25 = 825.75 cm². Rounding this to the nearest whole number yields 826 cm². The closest answer choice to 826 cm² is 817 cm², so there may be a discrepancy due to rounding in the available options.

Answer 2

Given:

Radii of two spheres are 3 cm and 4.5 cm respectively.

Surface area of the smaller sphere is 367 cm.

To find:

The surface area of the larger sphere.

Solution:

We know that, area of similar spheres is proportional to the square of there radii.

`(A_1)/(A_2)=((r_1)^2)/((r_2)^2)`

On substituting the values, we get

`(367)/(A_2)=((3)^2)/((4.5)^2)`

`(367)/(A_2)=(9)/(20.25)`

On cross multiplication, we get

`(367)(20.25)=9A_2`

`7431.75=9A_2`

Divide both sides by 9.

`(7431.75)/(9)=A_2`

`825.75 =A_2`

Therefore, the area of larger sphere is 825.75 cm².

Note: All options are incorrect.