Question

1. calculez le volume en pi³ de la forme présentée : ______ pi³

1. calculez le volume en pi³ de la forme présentée : ______ pi³

1. calculez la base (b) (linéaire) en pi de la forme présentée : ______ pi

Explanation:

Question 11

Step1: Convert all units to feet

10" = $\frac{10}{12} = \frac{5}{6}$ ft, 24" = $\frac{24}{12} = 2$ ft, 8'-0" = 8 ft, $r=10"=\frac{5}{6}$ ft

Step2: Calculate volume of rectangular prism

$V_{prism} = l \times w \times h = 2 \times 2 \times \frac{5}{6} = \frac{20}{6} = \frac{10}{3}$ ft³

Step3: Calculate volume of cylinder

$V_{cylinder} = \pi r^2 h = \pi \times (\frac{5}{6})^2 \times 8 = \pi \times \frac{25}{36} \times 8 = \frac{50\pi}{9}$ ft³

Step4: Total volume (sum both shapes)

$V_{total} = \frac{10}{3} + \frac{50\pi}{9}$
Convert $\frac{10}{3}$ to ninths: $\frac{30}{9} + \frac{50\pi}{9} = \frac{30 + 50\pi}{9} \approx 19.5$ ft³

Question 12

Step1: Identify prism dimensions

Base triangle: base $3'-0"=3$ ft, height $8'-0"=8$ ft; length of prism $10'-0"=10$ ft

Step2: Calculate area of triangular base

$A_{base} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 3 \times 8 = 12$ ft²

Step3: Calculate volume of prism

$V = A_{base} \times l = 12 \times 10 = 120$ ft³

Question 13

Step1: Convert height to feet

$9'-4" = 9 + \frac{4}{12} = 9 + \frac{1}{3} = \frac{28}{3}$ ft

Step2: Use slope formula to solve for base

Slope = $\frac{H}{B} \implies B = \frac{H}{\text{Slope}}$
$B = \frac{\frac{28}{3}}{\frac{5.5}{10}} = \frac{28}{3} \times \frac{10}{5.5} = \frac{28}{3} \times \frac{10}{\frac{11}{2}} = \frac{28}{3} \times \frac{20}{11} = \frac{560}{33} \approx 16.97$ ft

Answer:

1. $\frac{30 + 50\pi}{9}$ or approximately $19.5$ ft³
2. $120$ ft³
3. $\frac{560}{33}$ or approximately $17.0$ ft