1. The surface area of a cone can be calculated using the formula: SA = πr(r + l), where r is the radius and l is the slant height. Since the diameter is 14 inches, the radius is half of that, which is 7 inches. The slant height is given as 20 inches. Plugging these values into the formula, we get: SA = π(7)(7 + 20) = π(7)(27) = 7π(27) ≈ 595.94 square inches.
2. The volume of a cylinder can be calculated using the formula: V = πr^2h, where r is the radius and h is the height. The diameter is given as 12 inches, so the radius is half of that, which is 6 inches. Plugging these values into the formula, we get: V = π(6)^2(13) = π(36)(13) ≈ 1,507.96 cubic inches.
3. True. The diameter of a sphere is the longest distance across it, passing through the center.
4. The surface area of a sphere can be calculated using the formula: SA = 4πr^2. We are given that the surface area is 7.84π square feet. Setting up the equation and solving for r: 7.84π = 4πr^2. Dividing both sides by 4π and taking the square root, we get: r = √(7.84/4) ≈ 0.992 feet. Rounded to the tenths place and converted to feet, the radius of the ball is approximately 0.99 feet.
5. The volume of a sphere can be calculated using the formula: V = (4/3)πr^3, where r is the radius. We are given that the volume is 60 cubic meters. Setting up the equation and solving for r: 60 = (4/3)πr^3. Multiplying both sides by 3/4π and taking the cube root, we get: r = ∛(60/(3/4π)) ≈ 2.19 meters. Rounded to the hundredths place, the radius of the sphere is approximately 2.19 meters. The volume of the cylinder with the same dimensions can be calculated using the formula V = πr^2h, where r is the radius and h is the height. Plugging in the radius (2.19 meters) and height (2.19 meters), we get: V = π(2.19)^2(2.19) ≈ 20.81 cubic meters. Rounded to the hundredths place, the volume of the cylinder is approximately 20.81 cubic meters.
1. Cone has diameter of 14 inches and slant height of 20 inches. Find the surface area to nearesth hundredth. Need units.
2. Find volume of cylinder with diameter of 12 inches and height of 13 inches. (round to hundredth and include units)
3. T/F the diameter of the sphere is the longest distance on it?
4. Find radius of ball that has a surface area of 7.84𝝅 square feet. (round to tenth and units)
5, Volume of sphere is 60 cubic meters. Find volume of cylinder with same dimensions.
1 answer
1 answer