What is the volume of a hexagonal-based prism with a height of 12 in. and a base area of 62 in² ? Would the volume be different if the base were a pentagon with an area of 62 in² ? Explain.

Solution:

Given that,

Hexagonal-based prism with a height of 12 in. and a base area of 62 square inches

The volume of prism is given as:

Thus volume of a hexagonal-based prism is 744 cubic inches

Would the volume be different if the base were a pentagon with an area of 62 in² ?

No the volume will not be different

The shape of base does not matter, as long as the base area is same

Thus, volume of hexagonal-based prism and pentagon prism with area 62 inches is 744 cubic inches

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.