Question

A solid cube of side 7 cm is melted to make a cone of height 5 cm, find the radius of the base of the cone.​

Answer 1

Given:

⠀⠀⠀⠀⠀⠀

Side of the solid cube of 7 cm is melted to make a cone of height 5 cm.

⠀⠀⠀

⠀⠀⠀

To find:

⠀⠀⠀

⠀⠀⠀

Radius of the base of the cone.

⠀⠀⠀

⠀⠀⠀

Solution:

⠀⠀⠀

Volume of the cone = side × side × side = side$^{3}$

⠀⠀⠀

= 7 × 7 × 7

= 7$^{3}$ cm$^{3}$ = 343 cm$^{3}$

⠀⠀⠀

Now, we know that volume of cone = 1/3 $\pi$ r$^{2}$

⠀⠀⠀

= 1/3 × 22/7 × r$^{2}$ × 5 cm$^{3}$

⠀⠀⠀

According to the question, solid cube is melted to make the cone. So,

⠀⠀⠀

Volume of the cube = Volume of the cone

⠀⠀⠀

$\implies$ 343 = 1/3 × 22/7 × r$^{2}$ × 5

⠀⠀⠀

$\implies r {}^{2} = \frac{343 \times 3 \times 7}{22 \times 5} \\ \\ = \frac{7203}{110} = 65.48 \\ \\ \implies r = \sqrt{65.48} \: cm \\ \\ = 8.09 \: cm$

⠀⠀⠀

Thus, radius of the base of the cone is 8.09 cm

Answer 2

✦ Question :-

A solid cube of side 7 cm is melted to make a cone of height 5 cm, find the radius of the base of the cone.

✦ Given:

• Side = 7 cm

• Melted to make a cone { height = 5 cm }

✦ Find :-

What's the radius of the base of the cone ?

✦ Solution :-

As we know the volume of cube = ( side ) ³

⠀⠀⠀

Side = 7 cm ( FROM GIVEN )

↠ 7 × 7 × 7

↠ 7$^{3}$ cm$^{3}$ = 343 cm$^{3}$

⠀⠀⠀

Also we know other formula that volume of cone = 1/3 $\pi$ r$^{2}$

⠀⠀⠀

↠ 1/3 × 22/7 × r$^{2}$ × 5 cm$^{3}$

⠀⠀⠀

So, As in the Question say a solid cube is melted into cone so , the volume of cube should be equal to that of cone because it just turn from one shape into another .

⠀⠀⠀

{ Volume of Cube = Volume of cone }

⠀⠀⠀

$\implies$ 343 = 1/3 × 22/7 × r$^{2}$ × 5

⠀⠀⠀

$\implies r {}^{2} = \frac{343 \times 3 \times 7}{22 \times 5} \\ \\ = \frac{7203}{110} = 65.48 \\ \\ \implies r = \sqrt{65.48} \: cm \\ \\ = 8.09 \: cm$

⠀⠀⠀

Therefore ,

Radius of base of the cone is 8.09 cm

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .