The centre of a doughnut is removed and formed to make a sphere of dough with diameter 2.5 cm. A batch of these spheres is to be covered in a sugar glaze. There is enough glaze to cover an area of 4710 cm^2. How many spheres can be glazed?
A=4πr2
A = 4 * 3.14 * 1.25^2
A = 12.56 * 1.5625
A = 19.625 sq. cm.
4710 / 19.625 = _______ spheres
240 spheres
To find out how many spheres can be glazed, we first need to calculate the surface area of a single sphere.
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
In this case, we are given the diameter of the sphere, which is 2.5 cm. We can calculate the radius by dividing the diameter by 2:
Radius = diameter / 2 = 2.5 cm / 2 = 1.25 cm
Now we can substitute the value of the radius into the formula to find the surface area of a sphere:
Surface Area = 4π(1.25 cm)^2
Surface Area ≈ 4 × 3.14 × 1.25^2
Surface Area ≈ 4 × 3.14 × 1.5625
Surface Area ≈ 19.635 cm^2
Now that we know the surface area of a single sphere is approximately 19.635 cm^2, we can determine how many spheres can be glazed.
Given that there is enough glaze to cover an area of 4710 cm^2, we can divide the total available glaze area by the surface area of a single sphere to find the number of spheres that can be glazed:
Number of Spheres = Total available glaze area / Surface area of a single sphere
Number of Spheres = 4710 cm^2 / 19.635 cm^2
Using a calculator, we can find the approximate value:
Number of Spheres ≈ 239.956
Therefore, approximately 240 spheres can be glazed.
To find out how many spheres can be glazed, we need to determine the surface area of each sphere and then divide the total glaze area by that value.
The surface area of a sphere can be calculated using the formula: A = 4πr², where A represents the surface area and r is the radius.
Since we are given the diameter (2.5 cm) of the sphere, we can find the radius by dividing it by 2: r = d/2 = 2.5 cm / 2 = 1.25 cm.
Now let's calculate the surface area of the sphere using the formula:
A = 4π(1.25 cm)²
A = 4π(1.25 cm)(1.25 cm)
A ≈ 4π(1.56 cm²) (rounded to 2 decimal places)
A ≈ 6.28 cm²
So, the surface area of each sphere is approximately 6.28 cm².
To determine the number of spheres that can be glazed, we divide the total glaze area by the surface area of each sphere:
Number of spheres = Total glaze area / Surface area per sphere
Number of spheres = 4710 cm² / 6.28 cm²
Number of spheres ≈ 749.20
Since we cannot have a fraction of a sphere, we round down the result.
Therefore, the number of spheres that can be glazed is 749.