Question

1. A toy bucket is shaped like a cylinder with a diameter of 9 inches and a height of 12 inches. How much sand can the bucket hold? Use 3.14 for π.

Enter your answer, rounded to the nearest cubic inch, in the box.

2. Which pairs of polygons are similar? Select each correct answer.

3. What is the exact volume of a cylinder whose radius is 13 meters and whose height is 20 meters?
Enter your answer, in terms of π, in the box.

4. Which statements must be true? Select each correct answer.

5. This figure is made up of a triangle and a semicircle.
What is the area of the figure?
Use 3.14 for π.
Enter your answer, as a decimal, in the box.

Answer 1

Part 1) A toy bucket is shaped like a cylinder with a diameter of 9 inches and a height of 12 inches. How much sand can the bucket hold? Use 3.14 for π.

we know that
volume of a cylinder=pi*r²*h
diameter=9 in
r=9/2----> r=4.5 in
h=12 in
volume of a cylinder=pi*4.5²*12-----> 763.02 in³-----> 763 in³

the answer Part 1) is
763 in³

Part 2)Which pairs of polygons are similar? Select each correct answer.
see the attached figure with letters to better understand the problem

case A) are not similar, because one triangle is a equilateral triangle and the other is an isosceles triangle

case B)
18/8----> 2.25
24/15----> 1.6
the ratio of the measures of the lengths are different-----> are not similar

case C)
12.5/5---> 2.5
20/8-----> 2.5
7.5/3----> 2.5
30/12----> 2.5
the ratio of the measures of the lengths is equal-----> the pair is similar

case D)
22/13.75----> 1.6
16/10-----> 1.6
the ratio of the measures of the lengths is equal-----> the pair is similar

the answer Part 2) is
case C and case D are similar

part 3)What is the exact volume of a cylinder whose radius is 13 meters and whose height is 20 meters?
Enter your answer, in terms of π, in the box.

volume of a cylinder=pi*r²*h
r=13 m
h=20 m
volume of a cylinder=pi*13²*20----> 3380*pi m³

the answer part 3) is
the exact volume of a cylinder is 3380*pi m³

Part 4)
1) TM=RF----> is correct
2) m∠M=m∠F----> is correct
3) QM/BF=TM/RF----> is correct
4) QT/BR=TM/BF----> is not correct because QT/BR=TM/RF

Part 5)This figure is made up of a triangle and a semicircle.
What is the area of the figure?
Use 3.14 for π.

the diameter of the semicircle is 6 units
radius r=3 units
area of semicircle=pi*r²/2----> pi*3²/2----> 14.13 units²

area of triangle=b*h/2
b is equal to the diameter----> b=6 units
h is equal to 5 units
so area triangle=6*5/2----> 15 units²

area of the figure=14.13+15----> 29.13 units²

the answer is
the area of the figure is
29.13 units²