High School

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**Situation 5:**

Ivana is baking a round cake for a party using a cylindrical pan. The pan has a radius of 10 cm, and the cake's height will be 8 cm. Ivana needs to determine the amount of flour and other ingredients required to fill the pan with batter.

13. Calculate the area of the circular base to determine how much batter will cover the bottom of the pan.
14. What is the volume of the cake?

**Situation 6:**

Mrs. De Guzman assigns her students a project to build a pyramid-shaped model out of cardboard as part of their performance task. The pyramid has a square base with a side of 20 cm and a height of 30 cm.

15. What is the area of the square base?
16. What is the volume of the pyramid?

**Situation 7:**

Lenie wants to make pancakes for a snack. Her recipe requires 2 cups of flour, 1 ½ cups of milk, and 1 egg. Since she uses measuring tools with different units, she often needs to convert measurements. She noted that 1 cup is approximately equal to 240 mL.

17. How many mL of flour are needed according to her recipe?
18. If a can of milk contains 360 mL, how many cans of milk does she need?
19. If the recipe is doubled, how many liters of flour will be needed?
20. Lenie has a 5-liter container of flour. How many times can she make this recipe before she runs out of flour?

Answer :

Let's go through each situation step-by-step:

Situation 5:

  1. Calculate the area of the circular base of the cake pan:

The area [tex]A[/tex] of a circle is calculated using the formula:
[tex]A = \pi r^2[/tex]
where [tex]r[/tex] is the radius of the circle.

Here, the radius [tex]r = 10 \text{ cm}[/tex].

So, [tex]A = \pi (10)^2 = 100\pi \text{ cm}^2[/tex].

  1. Calculate the volume of the cake (cylinder):

The volume [tex]V[/tex] of a cylinder is given by:
[tex]V = \pi r^2 h[/tex]
where [tex]h[/tex] is the height of the cylinder.

Here, [tex]h = 8 \text{ cm}[/tex].

Thus, [tex]V = \pi (10)^2 (8) = 800\pi \text{ cm}^3[/tex].

Situation 6:

  1. Calculate the area of the square base of the pyramid:

The area [tex]A[/tex] of a square is:
[tex]A = s^2[/tex]
where [tex]s[/tex] is the side length of the square.

Here, [tex]s = 20 \text{ cm}[/tex].

So, [tex]A = (20)^2 = 400 \text{ cm}^2[/tex].

  1. Calculate the volume of the pyramid:

The volume [tex]V[/tex] of a pyramid is calculated by:
[tex]V = \frac{1}{3} A h[/tex]
where [tex]A[/tex] is the area of the base and [tex]h[/tex] is the height.

Here, [tex]A = 400 \text{ cm}^2[/tex] and [tex]h = 30 \text{ cm}[/tex].

Thus, [tex]V = \frac{1}{3} (400) (30) = 4000 \text{ cm}^3[/tex].

Situation 7:

  1. Convert cups of flour to mL:

The recipe requires 2 cups of flour. Since 1 cup is approximately 240 mL:

[tex]2 \text{ cups} = 2 \times 240 = 480 \text{ mL}[/tex]

  1. Determine how many cans of milk are needed:

The recipe needs 1 ½ cups of milk, which is:

[tex]1.5 \times 240 = 360 \text{ mL}[/tex]

Since a can of milk contains 360 mL, Lenie needs 1 can of milk.

  1. Determine how many liters of flour are needed if the recipe is doubled:

Doubling the flour means:

[tex]2 \times 480 \text{ mL} = 960 \text{ mL} = 0.96 \text{ L}[/tex]

  1. Calculate how many times Lenie can make the recipe with a 5-liter container of flour:

If the recipe uses 480 mL of flour, convert 5 liters to mL:

[tex]5 \text{ L} = 5000 \text{ mL}[/tex]

Lenie can make the recipe:

[tex]\frac{5000}{480} \approx 10.42[/tex]

Therefore, she can make the recipe 10 times before running out of flour.

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Rewritten by : Barada