Question

1. a) hexagonal pyramid b) trapezoidal prism c) cone d) square prism
2. a) cylinder b) rectangular prism c) triangular prism d) pentagonal prism

find the volume of each figure. round your answers to the nearest hundredth, if necessary.

1. a) 48.18 mi³ b) 33.51 mi³ c) 35.81 mi³ d) 268.08 mi³
2. a) 772.54 in³ b) 637.61 in³ c) 633.36 in³ d) 775.73 in³
3. a) 53 cm³ b) 147 cm³ c) 72 cm³ d) 49 cm³
4. a) 24 cm³ b) 16 cm³ c) 13 cm³ d) 27 cm³
5. a) 115.78 km³ b) 560 km³ c) 171.14 km³ d) 186.67 km³
6. a) 91 km³ b) 42 km³ c) 80 km³ d) 73 km³

Explanation:

Step1: Recall volume formulas

Volume of sphere $V = \frac{4}{3}\pi r^{3}$, volume of pyramid $V=\frac{1}{3}Bh$ (where $B$ is base - area and $h$ is height), volume of prism $V = Bh$.

Step2: Solve for problem 15

Given sphere with $r = 4$ mi. $V=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi(4)^{3}=\frac{4}{3}\pi\times64=\frac{256\pi}{3}\approx268.08$ mi³.

Step3: Solve for problem 16

Given sphere with $r = 5.7$ in. $V=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi(5.7)^{3}=\frac{4}{3}\pi\times185.193\approx772.54$ in³.

Step4: Solve for problem 17

For the pyramid with base dimensions $3$ cm and $7$ cm and height $7$ cm. Base - area $B = 3\times7 = 21$ cm². $V=\frac{1}{3}Bh=\frac{1}{3}\times21\times7 = 49$ cm³.

Step5: Solve for problem 18

For the triangular prism with base triangle having sides $3$ cm, $4$ cm, $5$ cm (right - triangle with base $b = 3$ cm and height $h = 4$ cm) and length $l = 4$ cm. Base - area of triangle $B=\frac{1}{2}\times3\times4 = 6$ cm². $V=Bh=6\times4 = 24$ cm³.

Step6: Solve for problem 19

For the pyramid with base dimensions $7$ km and $8$ km and height $10$ km. Base - area $B = 7\times8=56$ km². $V=\frac{1}{3}Bh=\frac{1}{3}\times56\times10=\frac{560}{3}\approx186.67$ km³.

Step7: Solve for problem 20

For the rectangular prism with dimensions $4$ km, $4$ km, and $5$ km. $V = l\times w\times h=4\times4\times5 = 80$ km³.

Answer:

1. D. 268.08 mi³
2. A. 772.54 in³
3. D. 49 cm³
4. A. 24 cm³
5. D. 186.67 km³
6. C. 80 km³