Which expression is equivalent to 4/9 x 7?
1 answer:
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Answer:
Only the second and third statements are correct:
Doubling <em>r</em> quadruples the volume.
Doubling <em>h</em> doubles the volume.
Step-by-step explanation:
The volume of a cylinder is given by:
We can go through each statement and examine its validity.
Statement 1)
If the radius is doubled, our new radius is now 2<em>r</em>. Hence, our volume is:
So, compared to the old volume, the new volume is quadrupled the original volume.
Statement 1 is not correct.
Statement 2)
Using the previous reasonsing, Statement 2 is correct.
Statement 3)
If the height is doubled, our new height is now 2<em>h</em>. Hence, our volume is:
So, compared to the old volume, the new volume has been doubled.
Statement 3 is correct.
Statement 4)
Statement 4 is not correct using the previous reasonsing.
Statement 5)
Doubling the radius results in 2<em>r</em> and doubling the height results in 2<em>h</em>. Hence, the new volume is:
So, compared to the old volume, the new volume is increased by eight-fold.
Statement 5 is not correct.
The surface area of the pentagonal prism is 648 square inches.
Step-by-step explanation:
Step 1:
The surface area of a shape is the sum of all the areas of all the external surfaces.
The pentagonal prism has a total of 7 sides i.e. 2 pentagonal sides and 5 rectangular sides.
The total surface area of the prism is the sum of the individual areas of the 7 sides.
Step 2:
The area of the 2 pentagonal sides square inches.
The area of each rectangular side is 80 square inches. So
The area of 5 rectangular sides square inches.
The total surface area of the prism square inches.
The surface area of the pentagonal prism is 648 square inches.