1. Suppose you want to buy concrete for a 36ft by 24 ft by 9 in. patio. If concrete costs $55/yd^3, how much will the concrete for the patio cost?
2. A cylinder has a volume of about 500 cm^3 and a height of 10 cm. What is the lenght of the radius to the nearest tenth of a cm?
500=3.14*R^2*10
500=31.4*R^2
R^2=500/31.4
R^2=15.92
R= √15.92
R=3.99 or 4 cm
To answer the first question, we need to calculate the volume of the patio and then convert it to cubic yards. Let's break it down into steps:
1. Calculate the volume of the patio:
- The dimensions of the patio are given as 36ft by 24ft by 9in.
- Since the height is given in inches, we need to convert it to feet. There are 12 inches in 1 foot, so 9 inches is equal to 9/12 = 0.75 feet.
- The volume of the patio is then calculated by multiplying the length, width, and height: 36ft * 24ft * 0.75ft.
2. Convert the volume to cubic yards:
- Since the cost of concrete is given as $55/yd^3, we need to convert the volume to cubic yards.
- There are 27 cubic feet in 1 cubic yard, so we divide the volume by 27: (36ft * 24ft * 0.75ft) / 27.
3. Calculate the cost of the concrete:
- Multiply the volume in cubic yards by the cost per cubic yard: [(36ft * 24ft * 0.75ft) / 27] * $55.
To answer the second question, we need to calculate the radius of the cylinder. Let's follow these steps:
1. Calculate the volume of the cylinder:
- The volume is given as 500 cm^3.
- The formula for the volume of a cylinder is V = π * r^2 * h, where V is the volume, r is the radius, and h is the height.
- Plug in the given values: 500 = π * r^2 * 10.
2. Rearrange the formula to solve for the radius:
- Divide both sides of the equation by (π * h): r^2 = 500 / (π * 10).
- Take the square root of both sides to find the radius: r = √(500 / (π * 10)).
3. Round the radius to the nearest tenth of a centimeter: Use a calculator to compute the value of r and round it to the nearest tenth place.
Now you should have the answers to both questions!
36 ft = 12 yards
24 ft = 8 yards
9 in = 0.25 yards
12 * 8 * 0.25 * 55 = ?
V=πr^2h
500 = 3.14 * r^2 * 10
Solve for r