a solid cube has side 8 CM. it is cut along diagonals of top face to get 4 equal parts. what is the total surface area of each part.
Answers
area of top surface is8×8=64
area of 1part =64÷4=16
When the cube shown above , is cut along diagonal FC , it will be divided into 2 right isosceles triangular prisms.
And when cut along diagonal DE, each piece will further be divided into 2 more isosceles right triangular prisms.
TO FIND: Total Surface area of Prism APBQDC
Top surface DCEF ia a square surface with each side 8 cm . <FDC = 90°
So, diagonal FC = √(8² + 8² ) = √128 = 8√2 cm
=> DQ = QC = 4√2 ( as diagonals of a square are equal & bisect each other at 90° angle.
Now, our required prism is APBDQC , which has following faces.
(1) Square ABCD , area = 8 * 8 = 64 cm²
(2) Rectangle APQD, area = 8 * 4√2 = 32√2 cm²
(3) Rectangle ABCQ, area = 8 * 4√2 = 32√2 cm²
(4) Isosceles Right triangle DQC, right angled at Q & DQ = CQ , area = 1/2* 4√2 * 4√2 = 16 cm²
(5) Similarly area ( triangle APB) = 16 cm²
So, total surface area = 64+32√2 +32√2+16+16
= 96 + 64√2
= 96 + 64* 1.41 = 96 + 90.24
= 186. 24 cm² ( approx)
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