Question

A solid metal sculpture in Kamila’s backyard is in the shape of a sphere and has a radius of 6 inches. She wants to have it melted and made into small solid cones. She would like the cones to each have a diameter of 6 inches and a height of 9 inches. With these dimensions, how many cones can be made from the metal sphere?

In your final answer, include all formulas, equations, and calculations necessary to determine how many cones can be made.

Answer 1

@gurrilabill @OrangeMaster

Answer 2

@elementwielder

Answer 3

well you 1st need to find the volume of the sphere... you know how to do that?

Answer 4

4/3 pi times radius cubed. So 288pi?

Answer 5

For the volume?

Answer 6

ya sorry... so keep it in terms of pi for now... next find the volume of one cone

Answer 7

Um how would I do that? I know it's 1/3 pi times radius squared times height, so would it be 72 pi?

Answer 8

For one cone?

Answer 9

i got 27pi

Answer 10

How

Answer 11

\[V= \frac{ \pi 3 ^{2} \times 9 }{ 3 }\]
=
\[\frac{ \pi \times9\times9 }{ 3 }\]
=
\[\frac{ 81\pi }{ 3 }\]
=
\[27\pi \]

Answer 12

Okay, so what do I do next?

Answer 13

divide 288 by 27

Answer 14

10.67

Answer 15

ya so you can make about 10 cones

Answer 16

Okay thank you so much! Can you help me with another one?

Answer 17

ya sure...

Answer 18

Each concrete block weighs 36.5 pounds. Each concrete block has two holes through the middle of the block. The holes are 4 inches wide by 4.5 inches long. If each block is solid concrete, how much would one block weigh?

Answer 19

@elementwielder

Answer 20

geez... i wouldnt know... im not good with weight conversions

Answer 21

Okay lol it's fine. What about this one: Kamila has a rectangular lawn that measures 80 by 150 feet. She wants to lay gravel made from colored rock in a border, 6 feet wide, all around the lawn. how many square feet of the gravel border will surround the lawn? Kamila decided that the depth of the gravel needs to be 2 inches. What is the total volume of gravel needed for the border? (Hint: dimensions must be in terms of the same unit before you can calculate the volume)
D. A large bag of colored rock contains of a cubic yard and costs $30. What is the total cost of the rocks needed for the border? (Hint: the volume of the border must be in terms of a cubic yard before you can calculate the cost)
In your final answers, include all formulas, equations, and calculations necessary to determine the correct answers.

Answer 22

Sorry it's so long

Answer 23

i can do the lawn one for now... ill answer D later if i can

Answer 24

Okay

Answer 25

What do you get for the lawn one? @elementwielder

Answer 26

sorry i just got unbanned

Answer 27

so your TOTAL dimensions will be 86 by 156... find the area of that and subtract the area of 80x150 from the TOTAL