Question

A piece of chocolate candy, composed of two congruent triangular prisms, is filled with caramel. If a = 1.8 cm, b = 1.1 cm, and c = 2.4 cm, how much caramel can fit inside the piece of candy? A. 2.376 cu cm B. 3.564 cu cm C. 4.752 cu cm D. 5.3 cu cm

Answer 1

The volume of the piece of candy is 2.376 cu cm.

Step-by-step explanation:

To find the volume of the piece of candy, we need to find the volume of two congruent triangular prisms and then subtract the volume of the caramel. The formula for the volume of a triangular prism is V = (1/2)A bh, where A is the area of the base, b is the base length, and h is the height.

Using the given dimensions a = 1.8 cm, b = 1.1 cm, and c = 2.4 cm, we can find the area of the triangular base using the formula for the area of a triangle: A = (1/2)bh.

Substituting the values, A = (1/2)(1.8 cm)(1.1 cm) = 0.99 cm².

The height of the prism is c = 2.4 cm.

Therefore, the volume of one prism is V = (1/2)(0.99 cm²)(2.4 cm) = 1.188 cu cm.

Since there are two congruent prisms, the total volume of the piece of candy is 2(1.188 cu cm) = 2.376 cu cm.

Answer 2

To calculate how much caramel can fit inside the chocolate candy, determine the volume of one triangular prism using the formula and then double it for both prisms. The total caramel volume is 4.752 cm³ (Option C).

Step-by-step explanation:

To find out how much caramel can fit inside the piece of chocolate candy made up of two congruent triangular prisms, we must calculate the volume of the triangular prism and then double it, as there are two prisms. The volume of a triangular prism can be found by the formula V = 1/2 × base × height × length. In this case, the base (a) is 1.8 cm, the height (b) is 1.1 cm, and the length (c) is 2.4 cm.

Using the formula, we calculate the volume of one prism:

V = 1/2 × 1.8 cm × 1.1 cm × 2.4 cm which gives V = 2.376 cm³.

Since there are two prisms, we double this value to get the total caramel volume:

4.752 cm³ (Option C).