How much bigger is a the volume of a cone with radius of 13 feet and a height of 30 feet than a cone with radius of 9 feet and a height of 30 feet? Use 3.14 for π.
The difference in the volumes of the cones is____ cubic feet.
Volume of first cone:
V1 = (1/3)πr1^2h1
V1 = (1/3)(3.14)(13^2)(30)
V1 = 5331.4 cubic feet
Volume of second cone:
V2 = (1/3)πr2^2h2
V2 = (1/3)(3.14)(9^2)(30)
V2 = 2544.6 cubic feet
Difference in volumes:
5331.4 - 2544.6 = 2786.8 cubic feet
Therefore, the difference in the volumes of the cones is 2786.8 cubic feet.
Find the volume of a cone with radius of 25 feet and a height of 18 feet. Use 3.14 for π.
The volume of the cone is cubic feet.
Volume of the cone formula is V = (1/3)πr^2h
Given:
Radius (r) = 25 feet
Height (h) = 18 feet
π = 3.14
Volume of the cone:
V = (1/3)(3.14)(25^2)(18)
V = (1/3)(3.14)(625)(18)
V = (1/3)(3.14)(11250)
V = (1/3)(35325)
V = 11775 cubic feet
Therefore, the volume of the cone is 11775 cubic feet.
Find the volume of a cone with diameter of 29 feet and a height of 24 feet. Use 3.14 for π.
The volume of the cone is cubic feet.
First, we need to find the radius of the cone using the given diameter:
Radius (r) = 1/2 * diameter
r = 1/2 * 29
r = 14.5 feet
Now we can use the formula for the volume of a cone:
V = (1/3)πr^2h
Given:
Radius (r) = 14.5 feet
Height (h) = 24 feet
π = 3.14
Volume of the cone:
V = (1/3)(3.14)(14.5^2)(24)
V = (1/3)(3.14)(210.25)(24)
V = (1/3)(3.14)(5046)
V = (1/3)(15883.64)
V = 5294.5467 cubic feet (rounded to 4 decimal places)
Therefore, the volume of the cone is approximately 5294.5467 cubic feet.
Find the surface area and volume of a sphere that has a radius of 72 inches. Use 3.14 for π. Do not round your answer.
The sphere's surface area is square inches.
The sphere's volume is cubic inches.
Given:
Radius (r) = 72 inches
π = 3.14
Surface area of a sphere:
A = 4πr^2
A = 4(3.14)(72^2)
A = 4(3.14)(5184)
A = 4(16259.36)
A = 65037.44 square inches
Volume of a sphere:
V = (4/3)πr^3
V = (4/3)(3.14)(72^3)
V = (4/3)(3.14)(373248)
V = (4/3)(1172296.32)
V = 1563055.0933 cubic inches
Therefore, the sphere's surface area is 65037.44 square inches and its volume is 1563055.0933 cubic inches.