MATHEMATICS
Directions: Find the volume of the following solids:
1. Rectangular Pyramid
Given:
- length of the base = 10 cm
- width of the base = 7 cm
- height of the pyramid = 16 cm
USE THIS FORMULA
[tex]V = \frac{1}{3} \: lwh[/tex]
SOLUTION
[tex]V = \frac{1}{3} \: lwh \\ V = \frac{1}{3}(10cm)(7cm)(16cm) \\ V = \frac{1}{3} (70 {cm}^{2} )(16 cm) \\ V = \frac{1}{3} (1120 {cm}^{3} ) \\ V = 373.33 \: {cm}^{3} [/tex]
FINAL ANSWER
[tex]V = 373.33 \: {cm}^{3} [/tex]
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2. Cylinder
Given:
USE THIS FORMULA
[tex]V = \pi {r}^{2} h[/tex]
SOLUTION
[tex]V = \pi {r}^{2} h \\ V = (3.14) {(6cm)}^{2} (10cm) \\ V = (3.14) ({36cm}^{2} )(10cm) \\ V = (3.14)(360 {cm}^{3} ) \\ V = 1,130.4 \: {cm}^{3} [/tex]
FINAL ANSWER
[tex]V = 1,130.4 \: {cm}^{3} [/tex]
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3. Cone
Given:
USE THIS FORMULA
[tex]V = \frac{1}{3} \pi {r}^{2} h[/tex]
SOLUTION
[tex]V = \frac{1}{3} \pi {r}^{2} h \\ V = \frac{1}{3}(3.14) {(8cm)}^{2} (12cm) \\ V = \frac{1}{3}(3.14)(64 {cm}^{2} )(12cm) \\ V = \frac{1}{3}(3.14)(768 {cm}^{3} ) \\ V = \frac{1}{3}(2,411.52 {cm}^{3} ) \\ V = 803.84 \: {cm}^{3} [/tex]
FINAL ANSWER
[tex]V = 803.84 \: {cm}^{3} [/tex]
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4. Sphere
Given:
USE THIS FORMULA
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]
SOLUTION
[tex]V = \frac{4}{3} \pi {r}^{3} \\ V = \frac{4}{3} (3.14) {(6cm)}^{3} \\ V = \frac{4}{3} (3.14)(216 {cm}^{3} ) \\ V = \frac{4}{3} (678.24 {cm}^{3} ) \\ V = 904.32 \: {cm}^{3} [/tex]
FINAL ANSWER
[tex]V = 904.32 \: {cm}^{3} [/tex]
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5. Square Pyramid
Given:
USE THIS FORMULA
[tex]V = \frac{1}{3} {s}^{2} h[/tex]
SOLUTION
[tex]V = \frac{1}{3} {s}^{2} h \\ V = \frac{1}{3} {(6cm)}^{2} (10cm) \\V = \frac{1}{3} (36 {cm}^{2} )(10cm) \\ V = \frac{1}{3} (360 {cm}^{3} )\\ V = 120 \: {cm}^{3} [/tex]
FINAL ANSWER
[tex]V = 120 \: {cm}^{3} [/tex]
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I hope it helps ^_^
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