Question

determine the volume of the entire figure:

hint: use the formula sheet to determine the formula(s) needed to solve the problem.

a. \\(710\text{ cm}^3\\)
b. \\(1,141\text{ cm}^3\\)
c. \\(637\text{ cm}^3\\)
d. \\(700\text{ cm}^3\\)

Explanation:

⚡ Using what you learned: volume of prisms, pyramids, cylinders, cones, spheres

Step 1: Volume of the rectangular prism

$$ V_{\text{prism}} = l \times w \times h $$

$$ V_{\text{prism}} = 7 \times 7 \times 10 = 490\text{ cm}^3 $$

Step 2: Volume of the square pyramid

$$ V_{\text{pyramid}} = \frac{1}{3} \times B \times h_{\text{pyramid}} $$

$$ B = 7 \times 7 = 49\text{ cm}^2 $$

$$ V_{\text{pyramid}} = \frac{1}{3} \times 49 \times 9 = 147\text{ cm}^3 $$

Step 3: Total volume of the composite figure

$$ V_{\text{total}} = V_{\text{prism}} + V_{\text{pyramid}} $$

$$ V_{\text{total}} = 490 + 147 = 637\text{ cm}^3 $$

Answer:

C. \(637\text{ cm}^3\)