A sphere has a surface area of 5554cm. Calculate the diameter of the sphere

Question

ScanSolve AI Tutor · Accepted Answer

Let's calculate the diameter of the sphere.

Write the formula for the surface area of a sphere.
$A = 4\pi r^2$
Substitute the given surface area ( $A = 5554 \text{ cm}^2$ ) into the formula.
$5554 \text{ cm}^2 = 4\pi r^2$
Rearrange the formula to solve for $r^2$ .
$r^2 = \frac{5554}{4\pi} \text{ cm}^2$ $r^2 = \frac{1388.5}{\pi} \text{ cm}^2$
Calculate the numerical value for $r^2$ (using $\pi \approx 3.14159$ ).
$r^2 \approx \frac{1388.5}{3.14159} \text{ cm}^2$ $r^2 \approx 442.09 \text{ cm}^2$
Take the square root to find the radius (r).
$r = \sqrt{442.09} \text{ cm}$ $r \approx 21.026 \text{ cm}$
Calculate the diameter (d) by multiplying the radius by 2.
$d = 2r$ $d \approx 2 \times 21.026 \text{ cm}$ $d \approx 42.052 \text{ cm}$
The diameter of the sphere is approximately 42.05 cm.

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