Question

If a person walks with a speed of 1.1 miles per hour, it takes 195 minutes to walk around the rim. Assuming that the rim is approximately a circle, what is the diameter of the crater? (Round your answer to the nearest tenth and make sure you convert the minutes to hours first!) b . How many cubic miles of sand would fill the crater if its approximate shape is a hemisphere (half of a sphere)? The volume of the whole sphere is V = 4 3 π r 3 . Round your answer to the nearest hundredth. cubic miles

Answer 1

a) 1.138 miles

b) 0.385 miles³

Explanation:

Data provided:

Speed = 1.1 miles per hour

Time taken to travel around the rim = 195 minutes

Now,

1 hour = 60 minutes

thus,

195 minutes =
`\frac{\textup{195}}{\textup{60}}` = 3.25 hours

Hence,

The total distance covered around the rim = speed × time

or

= 1.1 × 3.25

= 3.575 miles

a) Distance around the rim of crater = πd

where, d is the diameter of the crater

or

πd = 3.575

or

d = 1.138 miles

or

radius of the crater, r =
`\frac{\textup{d}}{\textup{2}}` =
`\frac{\textup{1.138}}{\textup{2}}` = 0.569 miles

b) Now

Volume of hemisphere =
`\frac{\textup{1}}{\textup{2}}*(\textup{volume of whole sphere})`

volume of whole sphere =
`\frac{\textup{4}}{\textup{3}}\pi r^3`

or

volume of whole sphere =
`\frac{\textup{4}}{\textup{3}}\pi*0.569^3`

or

volume of whole sphere = 0.771 miles³

Therefore,

The Volume of hemisphere =
`\frac{\textup{1}}{\textup{2}}*(\textup{0.771})`

or

The Volume of hemisphere = 0.385 miles³