The triangular prism has a volume of 27 cubic units.

what will be the volume of the prism if each side is dilated by a factor 1/3
1 cubic unit, 3,8,9

1 cubic unit will be the volume of the prism.

Step-by-step explanation:

Volume of the triangular prism = 27 cubic units

Since formula of volume of the triangular prism = (1/3)A×h

27 = (1/3)A×h ⇒ Ah = 27×3 = 81

Now each side of the prism is dilated then we have to calculate the volume of new prism.

V' = (1/3)×A'×h'

= (1/3) (1/9)A×(1/3)h = (1/81)×Ah = (1/81)×81 = 1 cubic unit

Therefore the volume of new prism will be 1 cubic unit

1 cubic unit

Step-by-step explanation:

We are given that

Volume of triangular prism= 27 cubic units

We are given that each side of triangular prism dilated by a factor of  1/3.

We have to find the new volume of triangular prism.

We have a relationship between the volumes

Where scale factor

= Volume of triangular prism after applying  the scale factor on each side

=Original volume of triangular prism

Substitute the values then we get

cubic unit

1 cubic unit

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

i believe the answer is c.