Volume
What is the volume of a sphere with a radius of 3.3 m, rounded to the nearest tenth of a cubic meter?
150.5 m^3
A metal cube has a volume of 125 cm^3 and a mass of 975 g. What is the density of the cube in g/cm^3?
7.8 g/cm^3
A rectangle has the length of (3x + 2) units and a width of (x+5) units. Find the perimeter of the rectangle in terms of x.
8x + 14
Solve using factoring:
x^2 - 5x + 6 = 0
x = 2 or x =3
A box-shaped container has a length of 10 cm, a width of 4 cm, and a height of 6 cm. What is the volume of the container?
240 cm^3
A Baja blast is served in a cup shaped like 2 stacked cylinders. Demir buys a Baja blast, the bottom cylinder has a radius of 5 cm and a height of 12 cm. The top cylinder has a radius of 3 cm and a height of 4 cm. What is the total volume of a baja blast in terms of Pi?
336π cm^3
A triangle has a base of (2x + 4) cm and a height of (x - 1) cm. Find the area of the triangle.
x^2 + x - 2
Solve using quadratic formula:
2x^2 + 3x - 5 = 0
x = 1 or x = -5/2
A water tank is shaped like a cylinder with a radius of 5 meters and a height of 12 meters. What is the volume of the tank rounded to the nearest tenth?
942.5 m^3
A rectangular block is 12 cm long, 8 cm wide, 6 cm high. A cylindrical hole with a radius of 2 cm and a height of 6 cm is drilled through the block. What is the volume of the block after the hole is drilled in?
500.6 cm^3
A rectangle has a length of (x + 4) and a width of x. A square with a side length x is cut out from the rectangle. What is the remaining area?
4x
Solve by factoring:
6x^2 - 13x + 6 = 0
x = 2/3 or x = 3/2
A square pyramid has a base length of 8 meters and a height of 15 meters. What is the volume of the pyramid?
320 m^3
An ice cream cone consists of a cone with a radius of 3 cm and a height of 10 cm, topped with a hemisphere of ice cream with the same radius. What is the total volume of the ice cream and cone?
150.8 cm^3
A garden is made of a rectangle and a semicircle.
Rectangle: length = 3x + 1, width = 2x -4
Semicircle diameter = rectangle width
Solve for area.
Reminder: area for circle = πr^2
6x^2 - 10x -4 +1/2π(x^2 - 4x +4)
Solve using quadratic formula:
x^2 = 7x -12
x = 4 or x = 3
A dome-shaped observatory is a hemisphere with a radius of 10 feet. What is the volume of the observatory to the nearest whole number?
2094 ft^3
A solid aluminum cylinder has a radius of 2 cm and a height of 10 cm. Aluminum has a density of 2.7 g/cm^3. What is the mass of the cylinder in grams?
339.3 g
The radius of a circle is given as (x + 2). Find the circumference in terms of x. (use C=2πr)
2πx + 4π
5x = x^2 + 6