Question

8 The circumference of circle B is 20% larger than the circumference of circle A.

Write down the ratio of the area of circle A to the area of circle B.
9 F and Gare mathematically similar greenhouses.
G
F has a volume of 5.6 m' and a surface area of 15 m².
The volume of G is 18.9m².
What is the surface area of G?

Answer 1

Explanation:

8.

circumference of circle B is 20% larger than A.

that means

circumference B = circumference A × 1.2

the circumference of a circle is

2pi×r

r being the radius.

the area of a circle is

pi×r²

2pi×rB = 2pi×rA × 1.2

rB = rA × 1.2

area of circle A

pi × (rA)²

area of circle B

pi × (rB)² = pi × (rA × 1.2)² = 1.44×pi×(rA)²

so the ratio of

area A / area B = pi×(rA)²/(1.44×pi×(rA)²) = 1/1.44 =

= 100/144 = 25/36 = (5/6)²

9.

there are clearly some typos in your definition.

let's clarify what the measurements have to be :

F has 5.6 m³ and 15 m².

G has 18.9 m³.

the volume of F and G have the factor

VF × f = VG

5.6 × f = 18.9

f = 18.9/5.6 = 3.375

since the area is a matter of squaring the dimensions, and the volume of cubing the dimensions, we get by pulling the cubic root of the factor f the scaling factor of the individual dimensions. and by squaring that again we get the scaling factor for the surface area.

the cubic root of 3.375 is 1.5.

the square of 1.5 is 2.25.

the surface area of G is then

15 × 2.25 = 33.75 m²