Question

the diameter d of a sphere is 19.2 cm. calculate the spheres surface area a. use the value 3.14 for π, and round your answer to the nearest tenth.

Explanation:

Step1: Find the radius

The radius \( r \) of a sphere is half of its diameter \( D \). So, \( r=\frac{D}{2} \). Given \( D = 19.2\) cm, then \( r=\frac{19.2}{2}=9.6 \) cm.

Step2: Recall the formula for surface area of a sphere

The formula for the surface area \( A \) of a sphere is \( A = 4\pi r^{2} \).

Step3: Substitute the values

We know \( \pi = 3.14 \) and \( r = 9.6 \) cm. Substitute these values into the formula: \( A=4\times3.14\times(9.6)^{2} \).
First, calculate \( (9.6)^{2}=92.16 \). Then, \( 4\times3.14 = 12.56 \). Now, multiply \( 12.56\times92.16 \).
\( 12.56\times92.16 = 12.56\times(90 + 2.16)=12.56\times90+12.56\times2.16 = 1130.4+27.1296 = 1157.5296 \).

Step4: Round to the nearest tenth

Rounding \( 1157.5296 \) to the nearest tenth gives \( 1157.5 \) (since the hundredth digit is 2, which is less than 5, we keep the tenth digit as it is).

Answer:

\( 1157.5 \)