Unit 13 L-7 Math 8
Aim: Use square root and cube root symbol to represent solutions to equations. (8.EE.2) Know the formulas
for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical
problems. (8.G.9)
Word Problems Involving Square and Cube Roots
You can use equations that involve square and cube roots to solve word problems. In some
situations only one of the square root solutions makes sense for the problem.
Area of a Circle
Volume of a Cone
A = πr2
!
V = ! πr2h
Volume of a Cylinder
Volume of a Sphere
V = πr2h
!
V = ! πr3
Exercise 1:
Amber wants to put carpet on the floor of her bedroom. The floor is a square with an area
of 182.25 square feet. How long should the piece of carpet be on each side?
Exercise 2:
A fully inflated beach ball contains 288 ! cubic inches of air. What is the radius of the
beach ball?
Exercise 3:
The area of a circle is 18.9! ft2. What is the radius of the circle to the nearest whole
number?
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Exercise 4:
The volume of a cube is 512 cubic centimeters. What is the area, in square centimeters,
of each side of the cube?
Exercise 5:
A square has a side length of 3x and an area of 324 in2 . What is the value of x?
Exercise 6:
Find the radius of a cylinder with a volume of 950 in3 and a height of 10 in. Round your
answer to the nearest tenth.
Exercise 7:
Find the radius of a cone with a volume of 196π cm3 and a height of 12 cm.
Exercise 8:
What is the diameter of a circle that has an area of 49π cm2?
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Unit 13 L-7 Math 8
Area of a Circle
Volume of a Cone
A = πr2
!
V = ! πr2h
Volume of a Cylinder
Volume of a Sphere
V = πr2h
!
V = ! πr3
Practice Problems:
For each question below, write an equation and solve it algebraically.
1. The area of a square is 144 cm2. What is the length of one side?
2. The area of a circle is 100 ! m2. What is the radius of the circle?
3. The volume of a cube is 343 cm3. What is the length of one side of the cube?
4. The area of a square is 289 m2. What is the perimeter of the square?
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5. Find the diameter of a circle whose area is 112 cm2. Round your answer to the nearest
tenth.
6. The volume of a sphere is 972 ! cm3. What is the radius of the sphere?
7. Find the radius of a cylinder with a volume of 208 cm3 and a height of 4 cm. Round your
answer to the nearest hundredth.
8. Find the radius of a cone with a volume of 175 in3 and a height of 21 in. Round your
answer to the nearest tenth.
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