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A spherical balloon has a surface area of 88cm2. What is the diameter of the balloon to the nearest tenth of a centimetre?

$\begin{array}{rcl} &\text{Surface Area of a Sphere } \\ &\boxed{~ \begin{array}{rcl} A &=& 4 \pi r^2 \qquad \text{diameter } d = 2r \quad r = \frac{d}{2} \\ A &=& 4 \pi \left( \frac{d}{2} \right) ^2 \\ A &=& 4 \pi \frac{d^2}{4} \\ A &=& \pi d^2 \\ \end{array}\\ ~}\\\\ \end{array}\\ \begin{array}{rcll} A &=& \pi d^2 \\ \pi d^2 &=& A \\ d^2 &=& \frac{A}{\pi} \qquad & | \qquad \sqrt{}\\ d &=& \sqrt{\frac{A}{\pi}} \qquad & | \qquad A = 88\ cm^2\\ d &=& \sqrt{\frac{88\ cm^2}{\pi}} \\ d &=& \sqrt{\frac{88}{\pi}} \ cm\\ d &=& 5.2925674284 \ cm\\ \end{array}\\$

The diameter of the balloon to the nearest tenth of a centimetre is 5.3 cm

567.89

Surface area of a sphere is:A=4.Pi.r^2

88=4.3.141592.r^2

88=12.566368.r^2

r^2=88/12.566368

r^2=7.00282 take the sqrt of both sides

r=2.64628cm-the radius of the balloon.

Diameter=2.64628 X 2=5.3cm-the diameter of the balloon.

Grade ten math is ridiculous. Why? Just why?

Because you need your balloon for the balloon festival and you need to make sure you have enough material !!

It is vitally important because if you do not get it right the balloon god will seek revenge !!!!