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

1 answer

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.