Question

Which statement is correct about a sphere?

It has exactly one great circle.

Its great circle has the same radius as the sphere.

The areas of its great circles through different planes are not equal.

The diameter of its great circle is double the diameter of the sphere.

Answer 1

any plane passing thru center creates a great circle. so a sphere has infinite great circles.

Answer 2

so you can strike off first option

Answer 3

Okay, I'm going to guess B?

Answer 4

and thats a very good guess :)

Answer 5

great circle radius = sphere radius

Answer 6

thats the oly correct option. last two options are incorrect.

Answer 7

Awesome, could you help me with some more?

Answer 8

sure :)

Answer 9

i would choose second

Answer 10

A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below.

What is the total volume of grains that can be stored in the silo?

34π ft3

68π ft3

136π ft3

152π ft3

Answer 11

lol i did this q like 20 times this year

Answer 12

Lol I've been working on it for like 2 days

Answer 13

First, see that its a mix of two shapes : cone, cylinder

Answer 14

both have same radius, r = 4/2 = 2

Answer 15

cylinder has height h = 8

Answer 16

cone has height h = 9.5 - 8 = 1.5

Answer 17

Right, I got that yesterday but somehow didn't get the right answer at the end

Answer 18

volime of silo = volume of cylinder + volume of cone

= \(\pi r^2 h + \frac{1}{3}\pi r^2 h\)

= \(\pi \ 2^2 8 + \frac{1}{3}\pi \ 2^2 1.5\)

= \(32 \pi + 2\pi \)

= \(34 \pi \)

Answer 19

see if it makes some sense :)

Answer 20

Yeah actually it does, lol thank you! You have time for more? (:

Answer 21

yea sure

Answer 22

Just tell me when you're sick of me haha

Answer 23

lol sure you're awesome carry on :)

Answer 24

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle.

Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle of radius 70 feet?

Answer 25

easy, use perimeter of circle formula

Answer 26

r = 70

Answer 27

perimeter = \(2 \pi r\)
= ?

Answer 28

wat ever u get, u need to divide it by 4, since it is a quarter circle.

Answer 29

What do I do first? lol

Answer 30

plugin r = 70 in above formula

Answer 31

Right, but then what do i do first in that formula

Answer 32

perimeter = \(2\pi r\)
= \(2 \pi . 70\)
= \(140 \pi\)

Answer 33

we need to divide it by 4 to get the quarter circle perimeter

Answer 34

perimeter of quarter circle = \(\frac{140 \pi}{4}\)
= ?

Answer 35

So 109.9?

Answer 36

you may want to leave it exact, instead of converting it to decimals

Answer 37

\(\frac{140 \pi}{4}\)

\(35 \pi\)

Answer 38

Nah my answers are in decimal form lol

Answer 39

@ganeshie8
A cylindrical piece of iron pipe is shown below. The wall of the pipe is 0.75 inch thick, and the pipe is open at both ends.

What is the approximate inside volume of the pipe?

Answer 40

lol ok then you're right :)

Answer 41

Alrighty, what about the one I just posted?

Answer 42

ok, id let u do this.. give it a try :)

Answer 43

Given, total diameter = 6

Answer 44

within that, how much goes waste for thickness ?

Answer 45

5.25?

Answer 46

careful, thickness is on both sides of diameter !

Answer 47

so you need to remove 0.75 two times

Answer 48

Okay so 4.50?

Answer 49

thats diameter of inner space.

Answer 50

wats the radius ?

Answer 51

2.25

Answer 52

Correct ! you have everything u need to use the formula :

volume of cylinder = \(\pi r^2 h\)

\(r = 2.25\)

\(h = 16\)

Answer 53

plugin

Answer 54

Alright so 254.34?

Answer 55

you have used \(\pi = 3.14\) is it

Answer 56

then yes you're right :D

Answer 57

It's easy once I know what to do lol. How would I find the volume of this one?
A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 marbles, each of diameter 2 inches. The vase is filled with water up to a height of 12 inches.

What is the volume of water in the vase?

Answer 58

two steps

Answer 59

step 1 : find the volume of marbles

Answer 60

step 2 : find the volume of water including marbles

Answer 61

step 3 : subtract 1 from 2

Answer 62

ok those are 3 steps lol

Answer 63

... 9 marbles, each of diameter 2 inches.

Answer 64

diameter = 2, so r = 1

Answer 65

volume of one marble = \(\frac{4}{3} \pi r^3 \)
= \(\frac{4}{3} \pi 1^3 \)
= \(\frac{4}{3} \pi \)

Answer 66

volume of 9 marbles = \(9 \times \frac{4}{3} \pi \)\)
= \(12 \pi\) -----------------------(1)

Answer 67

you wid me so far ha

Answer 68

I'm trying lol

Answer 69

ok we're done wid step1. lets move to step2

Answer 70

The vase is filled with water up to a height of 12 inches.

So, volume of water including marbles = \(\pi r^2 h\)
= \(\pi 3^2 12\)
= \(108 \pi \) ------------------(2)

Answer 71

volume of water alone = (2) - (1)
= \(108\pi - 12\pi\)
= ?

Answer 72

376.80

Answer 73

check again

Answer 74

96?