A prism of equilateral triangular base of area 64 sq.cm and ht. 9 cm is melt and made into a cube...What is it's total surface area?
2006-07-09 17:35:10 · 3 answers · asked by sangeetha e 1 in Science & Mathematics ➔ Mathematics
To solve this problem you need to understand three formulas.
1st: The volume of the prism is the area of the base times the height. so 64 * 9 = 576 cm.cubed.
2nd: The volume of a cube is S^3 (where S is the measure of a side. So if S^3 = 576 then S = 576^1/3 (cube root of 576). Or about 8.32.
3rd: to find the surface area of a cube, find the area of one side and multiply by 6. 8.32 * 8.32 * 6 = 415 sq.cm
2006-07-09 18:01:44 · answer #1 · answered by knowbody 1 · 0⤊ 0⤋
So the volume of this prism is 64•9. The side length of a cube with volume 64•9 is (64•9)^(1/3)=4(9^(1/3)) cm. The surface area of this cube is then 6•(4(9^(1/3)))^2=96•9^(2/3) sq cm.
2006-07-10 00:46:01 · answer #2 · answered by Eulercrosser 4 · 0⤊ 0⤋
Volume of the material (prism) = 64*9 = 576 cm³
the cube parameter L= ³âV
L = 8.32 cm
A =6 L²
A = 415.368 cm²
2006-07-10 01:20:17 · answer #3 · answered by M. Abuhelwa 5 · 0⤊ 0⤋