A rectangular parallelepiped with a volume of 396 cm³ has one of its faces which is a rectangle measuring 4.5 cm by 8 cm. What is its third dimension?
Answers
Given :-
◉ Dimensions of Parallelepiped, 4.5 cm by 8 cm
Describing in vectors components form, we have
A = 4.5i
B = 8j
C = xk
Let the component of k of the vector C be x.
◉ Volume of Parallelepiped = 396 cm³
To Find :-
◉ Third dimension of Parallelepiped
Solution :-
We have,
A = 4.5i , B = 8j , C = xk
First, Let us find B × C ,
| i j k |
⇒ B × C = | 0 8 0 |
| 0 0 x |
⇒ B × C = (8 - x)i - (0 - x)j + 0k
⇒ B × C = (8 - x)i + xj ...(1)
We know,
⇒ Volume of Parallelepiped = [ABC]
⇒ 396 = A . ( B × C )
⇒ 396 = (4.5i) . { (8 - x)i + xk }
⇒ 396 = 4.5(8 - x) + 4.5 × 0 + 0 × x
⇒ 396 = 36 - 4.5x
⇒ 360 = -4.5x
⇒ x = -360/4.5
⇒ x = -80
Hence, The third dimension is -80k.
Parallelepiped = 4.5i + 8j - 80k
Answer:
⚫ Dimensions of parallelepiped 4.5 cm by 8 cm.
Describe in vector components form we have,
✏ A = 4.5 I
✏ B = 8 j
✏ C = xk
⚫ Volume of parallelepiped = 396cm³.
➡ To find:-
Three dimensional of parallelepiped
➡ SOLUTION:-
We have,
A= 4.5 l , B= 8 j , C = xk
⭐ First, let us find B × C
| ijk |
=> B× C = | 080 |
= | 00x |
=> B×C = (8-x)I - (0-x)j + 0k
=> B×C = (8-x)I + xj. .....(1)
We have,
=> Volume of parallelepiped = [ABC]
=> 396 = A. (B×C)
=> 396 = (4.5i) . {(8-x)I + xk
=> 396 = 4.5(8-x) +4.5×0+0×x
=> 396 = 36 - 4.5x
=> x= - 80
⭐ Hence, the third dimension is -80k
⭐ Parallelepiped = 4.5i +8j-80k
Step-by-step explanation: