Question

the formula for the surface area of a sphere is 4piR^2. sphere A has a radius of 3cm and sphere b has a radius of 6cm. calculate the surface area of each sphere and compare their surface areas

Answer 1

To calculate the surface area of each sphere, we can use the formula for the surface area of a sphere:

\[ \text{Surface Area} = 4\pi R^2 \]

where \( R \) is the radius of the sphere.

**For Sphere A:**
- Radius (\( R \)) = 3 cm

\[
\text{Surface Area of Sphere A} = 4\pi (3)^2 = 4\pi \cdot 9 = 36\pi \, \text{cm}^2
\]

**For Sphere B:**
- Radius (\( R \)) = 6 cm

\[
\text{Surface Area of Sphere B} = 4\pi (6)^2 = 4\pi \cdot 36 = 144\pi \, \text{cm}^2
\]

**Comparison of Surface Areas:**
- Surface Area of Sphere A: \( 36\pi \, \text{cm}^2 \)
- Surface Area of Sphere B: \( 144\pi \, \text{cm}^2 \)

To compare their surface areas, we can find the ratio of the surface areas:

\[
\text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{144\pi}{36\pi} = \frac{144}{36} = 4
\]

This means that Sphere B has a surface area that is 4 times greater than that of Sphere A.

In conclusion:
- Surface Area of Sphere A = \( 36\pi \, \text{cm}^2 \)
- Surface Area of Sphere B = \( 144\pi \, \text{cm}^2 \)
- Sphere B's surface area is 4 times larger than Sphere A's surface area.