Aglobe company currently manufactures a globe that is 20 inches in diameter. if the dimensions of the globe were reduced by half, what would its volume be? use 3.14 for π and round your answer to the nearest tenth.

The volume of the reduced globe is

Step-by-step explanation:

step 1

we know that

The volume of a sphere is equal to

we have

-----> the radius is half the diameter

substitute

The volume of the original globe is

step 2

If the dimensions of the globe were reduced by half,

then

The new radio is equal to

The volume of the reduced globe is

therefore

The volume of the reduced globe is

Compare the volumes

Remember that

If two solids are similar, then the ratio  of its volumes is equal to the scale factor elevated to the cube

The scale factor is 1/2

so

therefore

The original globe is eight times the volume of the reduced globe

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2