Sara has a stack of 8 plates each plate is 0.5 inches and she is trying to wrap them as a gift the largest plate has a diameter of 10 inches and each plate has a diameter of 1 inch smaller than the previous plate. She has a cylindrical box with a radius of 5 in that can hold 150 cubic inches will her plates fit in the box

No her plates will not fit in the box

Step-by-step explanation: Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of .

Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.

What we want to figure out now is the height of the cylindrical box to see if it is greater than or equal to 4 inches—the height of the stack of plates.

The volume of a cylinder is , and since for our cylindrical box the volume is 150 cubic inches; therefore,

putting in  and solving for height  we get

,

which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.

x = 25/2304

step-by-step explanation:

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours