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Math

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PROBLEM

Find the volume of the prism below.

STEP 1

1. The prism is L-shaped.
2. The vertical section of the L-shape is 4 4 cm high and 8 8 cm wide.
3. The horizontal section of the L-shape is 1 1 cm high and 8 8 cm wide.
4. The entire base length of the L-shape is 16 16 cm.

STEP 2

1. Break down the L-shaped prism into two rectangular sections.
2. Calculate the volume of each section.
3. Sum the volumes of the two sections to find the total volume.

STEP 3

Break down the L-shaped prism into two rectangular sections:
- Section 1: The vertical section with dimensions 4 4 cm (height) by 8 8 cm (width) by 8 8 cm (depth).
- Section 2: The horizontal section with dimensions 1 1 cm (height) by 8 8 cm (width) by 8 8 cm (depth).

STEP 4

Calculate the volume of each section:
- Volume of Section 1:
V1=Height×Width×Depth V_1 = \text{Height} \times \text{Width} \times \text{Depth} V1=4 cm×8 cm×8 cm V_1 = 4 \text{ cm} \times 8 \text{ cm} \times 8 \text{ cm} V1=256 cm3 V_1 = 256 \text{ cm}^3 - Volume of Section 2:
V2=Height×Width×Depth V_2 = \text{Height} \times \text{Width} \times \text{Depth} V2=1 cm×8 cm×8 cm V_2 = 1 \text{ cm} \times 8 \text{ cm} \times 8 \text{ cm} V2=64 cm3 V_2 = 64 \text{ cm}^3

SOLUTION

Sum the volumes of the two sections to find the total volume:
Vtotal=V1+V2 V_{\text{total}} = V_1 + V_2 Vtotal=256 cm3+64 cm3 V_{\text{total}} = 256 \text{ cm}^3 + 64 \text{ cm}^3 Vtotal=320 cm3 V_{\text{total}} = 320 \text{ cm}^3 The volume of the L-shaped prism is:
320 cm3 \boxed{320 \text{ cm}^3}

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