MATH SOLVE

5 months ago

Q:
# which has the greatest surface area two pizza that have 14 inch diameters or one pizza that has a 20 inch diameter

Accepted Solution

A:

Surface area of a pizza can be calculated using the same formula as area of a circle.

Formula of area of circle: 2 Γ pie Γ radius^2

[tex]2\pi{ r}^{2} [/tex]

A 14 inch diameter pizza has a radius of 14 inch Γ· 2 = 7 inch.

Surface area of one 14 inch pizza:

[tex]2\pi {7}^{2} \\ = 2\pi49 \\ = 2 \times 49 \times \pi \\ = 98\pi[/tex]

Surface area of two 14 inch pizzas:

[tex]98\pi \times 2 \\ = 196\pi[/tex]

Surface area of one 20 inch pizza:

[tex]2\pi { \frac{20}{2} }^{2} \\ = 2\pi {10}^{2} \\ = 2\pi100 \\ = 200\pi[/tex]

Compare the coefficients of pie, or the number towards the left of pie. The number is greater for the 20 inch pizza, since 200 > 196, 200pie > 196pie. 20 inch pizza has greater surface area than two 14 inch pizzas.

Hope this helps! :)

Formula of area of circle: 2 Γ pie Γ radius^2

[tex]2\pi{ r}^{2} [/tex]

A 14 inch diameter pizza has a radius of 14 inch Γ· 2 = 7 inch.

Surface area of one 14 inch pizza:

[tex]2\pi {7}^{2} \\ = 2\pi49 \\ = 2 \times 49 \times \pi \\ = 98\pi[/tex]

Surface area of two 14 inch pizzas:

[tex]98\pi \times 2 \\ = 196\pi[/tex]

Surface area of one 20 inch pizza:

[tex]2\pi { \frac{20}{2} }^{2} \\ = 2\pi {10}^{2} \\ = 2\pi100 \\ = 200\pi[/tex]

Compare the coefficients of pie, or the number towards the left of pie. The number is greater for the 20 inch pizza, since 200 > 196, 200pie > 196pie. 20 inch pizza has greater surface area than two 14 inch pizzas.

Hope this helps! :)