Cones and Cubes

Geometry Level 1

A piece of metal in the form of a cone of radius 3cm and height 7cm is melted and cast into a cube. Find the side of the cube(nearest to a whole number).


The answer is 4.

Milind Prabhu by milind prabhu , 21, India

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6 solutions

Lavanya Lavs
Mar 21, 2014

4 approx

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Shreyas Shastry
Mar 5, 2014

it is said that a cone is melted and is re cast into a cube

so we can say that volume of the cube is same as the volume of the cone

so by using v=1/3x22/7x3x3x7

it come to v=66

we know the formula to find volume of cube is l^3

so we have l^3=66

and l=4.04

which comes to 4

1 Helpful 0 Interesting 0 Brilliant 0 Confused

good one, buddy...

MOHD NAIM MOHD AMIN - 7 years, 3 months ago

volume of cone= pi r^2 (h/3) = 3.14 9*7/3 = 65.94 cubic cm volume of cube = a^3 a^3 = 65.94 a = cube root(65.94) a= 4.04002 = 4 approximately So side of cube is 4 cm.

Siva Gonam - 7 years, 1 month ago
Uahbid Dey
Apr 19, 2014

V = (⅓)πr²h = 65.9734 cc => a³ = 65.9734 => a = 4.04 cm = 4 cm (approx.)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Hello and hi,

So 1st of all,we will equate both volume of a cone and and volume of cube,

as volume of a cone=volume of a cube, after being melted,

1/3 x pie x radius ^ 2 x h = length of the cube's side ^ 3

(1/3 x pie x 3 ^ 2 x 7 ) ^ 1/3 = length of the cube's side

length of the cube's side = 4.00 cm(approximately)...

thanks...

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Annu Ben
Mar 5, 2014

surface area of cone=22/7 3(3+7) 22/7 3*10=660/7=94.2 so we can take 93 as SA of cube one side of cube =4

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Venture Hi
Mar 4, 2014

x^3= 1/3 pi 9*7

x=4.04...

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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