Jared baked a cake for his sister's birthday and is trying to figure out how much frosting he will need to decorate it. The cake has a diameter of and a height of .
If he only wants to frost the top and the sides of the cake, how much frosting will he need? Use .
Area to be frosted
First, we need to calculate the surface area of the top and sides of the cake that Jared wants to frost.
Surface area of the top of the cake:
The top of the cake is a circle with a diameter of , so the radius () is half of the diameter:
= / 2
= / 2
=
The area of the top of the cake is:
= πr^2
= π × ()^2
= π × ()^2
= π ×
Surface area of the sides of the cake:
The sides of the cake form a cylinder with a radius of and a height of :
Circumference of the cake = × = πd
= π ×
= 2π
The area of the sides of the cake is:
= ×
= ×
=
Total frosting needed:
Total frosting needed = Area of the top of the cake + Area of the sides of the cake
Total frosting needed = +
Total frosting needed = +
Total frosting needed =
So, Jared will need approximately of frosting to decorate the top and sides of the cake.
Jared baked a cake for his sister's birthday and is trying to figure out how much frosting he will need to decorate it. The cake has a diameter of 20cm and a height of 8cm .
If he only wants to frost the top and the sides of the cake, how much frosting will he need? Use pi to help you get the right answer .
Area to be frosted
First, we need to calculate the surface area of the top and sides of the cake that Jared wants to frost.
Surface area of the top of the cake:
The top of the cake is a circle with a diameter of 20 cm, so the radius () is half of the diameter:
= / 2
= / 2
= 10 cm
The area of the top of the cake is:
= πr^2
= π × ()^2
= π × (10)^2
= π × 100
= 100π cm^2
Surface area of the sides of the cake:
The sides of the cake form a cylinder with a radius of 10 cm and a height of 8 cm:
Circumference of the cake = × = πd
= π × 20 cm
= 20π cm
The area of the sides of the cake is:
= ×
= ×
= 160π cm^2
Total frosting needed:
Total frosting needed = Area of the top of the cake + Area of the sides of the cake
Total frosting needed = 100π + 160π
Total frosting needed = 260π cm^2
Therefore, Jared will need 260π cm^2 of frosting to decorate the top and sides of the cake.