Math / Geometry

QuestionFind the volume of the prism below.

Studdy Solution

STEP 1

1. The prism is L-shaped.
2. The vertical section of the L-shape is $4$ cm high and $8$ cm wide.
3. The horizontal section of the L-shape is $1$ cm high and $8$ cm wide.
4. The entire base length of the L-shape is $16$ 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 $4$ cm (height) by $8$ cm (width) by $8$ cm (depth). - Section 2: The horizontal section with dimensions $1$ cm (height) by $8$ cm (width) by $8$ cm (depth).

STEP 4

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

STEP 5

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

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