Please help me
1.The surface are of the exterior of hollow rubber ball is 16pi in^2.The rubber is 1/4 inch thick. Find the surface are of the interior of the ball.
2. The length of each side of a cube is 6 inches long. Find the exact area of a sphere inscribed in the cube.
Sure, I'll be happy to help you with these questions!
1. To find the surface area of the interior of the hollow rubber ball, we first need to find the radius of the exterior surface. We know that the surface area of the exterior of the hollow ball is given as 16π in^2. The formula for the surface area of a sphere is 4πr^2, where r is the radius. Since the rubber is 1/4 inch thick, the exterior radius will be the sum of the interior radius and the thickness of the rubber.
Let's assume the interior radius is r. Then the exterior radius will be (r + 1/4). Given that the surface area of the exterior of the ball is 16π in^2, we can set up the equation:
4π(r + 1/4)^2 = 16π
To solve this equation, we can simplify it first:
(r + 1/4)^2 = 4
Taking the square root of both sides:
r + 1/4 = 2
r = 2 - 1/4
r = 7/4
Now that we have the radius of the interior surface, we can calculate its surface area using the formula 4πr^2:
Surface Area = 4π(7/4)^2 = 4π(49/16) = (196/16)π = 49π/4
Therefore, the surface area of the interior of the hollow rubber ball is 49π/4 square inches.
2. To find the exact area of a sphere inscribed in a cube, we need to determine the radius of the sphere. In this case, the length of each side of the cube is given as 6 inches. A sphere is inscribed in a cube when the diameter of the sphere is equal to the edge length of the cube.
Since the edge length of the cube is given as 6 inches, the diameter of the sphere is also 6 inches. The formula for the volume of a sphere is (4/3)πr^3, and the formula for the area of a sphere is 4πr^2.
To find the radius, we divide the diameter by 2:
Radius = 6/2 = 3 inches
Now we can find the area of the sphere using the formula 4πr^2:
Area = 4π(3)^2 = 4π(9) = 36π
Therefore, the exact area of the sphere inscribed in the cube is 36π square inches.
evidently r=4
so, the inside radius is 3.75
The inside area is 4pi * 3.75^2
The inscribed sphere has a diameter of 6, and a radius of 3.
v = 4/3 pi r^3
plug and chug
also, the length is not six inches long. Each side is six inches long; the length is just six inches.