Question

Unit 11: volume & surface area homework 7: volume of prisms & cylinders

Answer 1

The volumes of the solids can be found by using the volume formula for

regular solids.

Responses:

1. 1,568 in.³
2. 60 cm.³
3. 2,521.91 mm³
4. 13,364 cm³
5. 3,150 ft.³
6. 257.36 km.³
7. 1,795.5 cm.³
8. 374.13 in.³
9. 347.82 yd.³
10. 2,105.87 m³
11. 1,060.02 mm³
12. 14 ft.
13. 23 in.
14. 3,861 cm³

Which method can be used to find the volume of solid shapes?

1. The given shape is a cube

Length = 17.5 in.

Width = 14 in.

Height = 6.4 in.

Volume = 17.5 in. × 14 in. × 6.4 in. = 1,568 in.³

2. Triangular prism

Height of triangle = 3.6 m

Base length = 10 m

Width of prism = 5 m

$Volume = \mathbf{ \dfrac{1}{2} \times 10 \, m \times 3.6 \, m \times 5 \, m }= \underline{60 \, m^3}$

3. Diameter of cylinder = 13 mm

Height of cylinder = 19 mm

$Volume = \mathbf{ \pi \times \dfrac{(13 \, mm)^2}{4} \times 19 \, mm }\approx \underline{2,521.91 \, mm^3}$

4. Trapezoidal prism

$Volume = \mathbf{ \dfrac{15 \, cm+ 37 \, cm}{2} \times 25.7 \, cm \times 20 \, cm} = \underline{13,364 \, cm^3}$

5. Rectangular prism

Volume = 18 ft. × 25 ft. × 7 ft. = 3,150 ft.³

6. Cylinder

$Volume = \mathbf{ \pi \times (3.2 \, km)^2 \times 8 \, km} \approx \underline{ 257.36 \, km^3}$

7. Trapezoidal prism

$Volume = \mathbf{ \dfrac{11 \, m + 16 \, m }{2} \times 9.5 \, m \times 14 \, cm} = \underline{ 1,795.5 \, cm^3}$

8. Hexagonal prism

Base area = 41.57 in.²

Volume = 41.57 in.² × 9 in. = 374.13 in.³

9. Triangular prism

Height of triangle = $\mathbf{ \sqrt{(15.7 \, yd.)^2 - (8.5 \, yd.)^2} }$ = 13.2 yd.

$Volume = \mathbf{ \dfrac{1}{2} \times 8.5 \ yd. \times 13.2 \ yd. \times 6.2 \ yd. }= \underline{347.82 \ yd.^3}$

10. Cylinder

Diameter = $\mathbf{ \sqrt{(19.3 \, m)^2 - (9.5 \, m)^2}}$ = 16.8 m

$Volume = \mathbf{ \pi \times \dfrac{ (16.8 \, m)^2}{4} \times 9.5 \, m} \approx \underline{2,105.87 \ m^3}\alpha$

11. Equilateral triangle prism

$Volume = \mathbf{ \dfrac{\sqrt{3} }{4} \times (12 \, mm)^2 \times 17 \, mm} \approx \underline{ 1,060.02 \, mm^3}$

12. Volume of rectangular prism = 655.2 ft.³

Dimensions of the bade = 9 ft. by 5.2 ft.

Therefore;

$Height = \mathbf{ \dfrac{655.2 \, ft.^3}{9 \, ft. \times 5.2 \, ft.} } = \underline{14 \, ft.}$

13. Height of the cylinder = 7 inches

Volume = 2,908.33 in.³

$Diameter = \mathbf{ \sqrt{\dfrac{ 4 \times 2,908.33 \ in.^3}{7 \ in. \times \pi} }} \approx \underline{23 \ in.}$

14. The composite figure consisting of a rectangular prism and a trapezoidal prism

$Volume = \mathbf{ 17 \times 13 \times 8 + \dfrac{6 + 17}{2} \times (22 - 8) \times 13} = 3861$

The volume is 3,861 cm³

Learn more about the volume of regular shapes here:

https://brainly.com/question/1621908

Answer 2

Answer:

2 is actually 90 cm cubed

Step-by-step explanation:

If you do the math given in the step by step directions it equals 90