Mary is making a piñata that has a ball-like shape. The piñata has a surface area of 40 square feet. Use the formula for the surface area of a sphere: [tex]S = 4\pi r^2[/tex] to find the radius of the piñata. Round your answer to the nearest hundredth.

S = 4 π r 2 an d S = 40 [ f ee t ] ⇒ 4 π r 2 = 40 / : 4 π r 2 = π 10 ​ ⇒ r = π 10 ​ ​ ⇒ r ≈ 1.78 [ f ee t ]

Answered by kate200468 | 2024-06-10

The radius of the sphere-shaped piñata with a surface area of 40 feet is approximately 1.78 feet, calculated using the surface area formula for a sphere.
To find the radius of the piñata with a given surface area, we can use the formula for the surface area of a sphere, which is S = 4πr². We know that the surface area S is 40 feet. Substituting this value into the formula, we get 40 = 4πr². To solve for r, we then divide both sides of the equation by 4π to get r² = 40 / (4π). Taking the square root of both sides gives us the radius r. Using a calculator, we can find the numerical value of r and round it to the nearest hundredth.
Let's go through the steps now:
Divide the surface area by 4π: r² = 40 / (4π).
Calculate r²: r² = 3.183098861.
Take the square root of r²: r = √(3.183098861).
Round r to the nearest hundredth: r = 1.78 feet.
Therefore, the radius of the sphere-shaped pinata is approximately 1.78 feet.

Answered by PragatiR | 2024-06-24

The radius of the piñata is found to be approximately 1.78 feet using the formula for the surface area of a sphere. We substituted the given surface area into the formula, isolated the radius, and calculated its value. This involved approximating π to evaluate the square root accurately.
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Answered by kate200468 | 2024-12-23