Question

A prism of height 12" has a rhombus with diagonals 6" and 8" for a base. Find the volume. 240 cu. in. 288 cu. in. 576 cu. in.

Answer 1

its not 576 because i got it wrong

Answer 2

Option 2nd is correct

volume of prism is, 288 cu. in.

Explanation:

Volume of prism(V) is given by:

`V = B \cdot h` .....[1]

where,

B is the Base area

h is the height of the prism.

Area of rhombus(A) is given by:

`A = (1)/(2)d_1 \cdot d_2`

where,

`d_1, d_2` are the diagonals of the rhombus.

As per the statement:

A prism of height 12" has a rhombus with diagonals 6" and 8" for a base.

⇒
`d_1 = 6`,
`d_2= 8` and h = 12"

Find the base area i.,e Area of rhombus.

`B = (1)/(2)(6 \cdot 8)`

Simplify:

`B = 24` square inches.

Substitute the given values in [1] we have;

`V = 24 \cdot 12 = 288` cubic inches.

Therefore, the volume of prism is, 288 cu. in.