Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Let's carefully analyze Lara's work and correct any mistakes she might have made.
1. Lara used the formula for the volume of a sphere: [tex]\(V = \frac{4}{3} \pi r^3\)[/tex].
2. However, she used the diameter ([tex]\(d = 10\)[/tex]) directly in the formula instead of the radius ([tex]\(r\)[/tex]). The radius of a sphere is half of the diameter. So for a diameter of 10, the radius [tex]\(r = \frac{10}{2} = 5\)[/tex].
3. Rewriting the volume formula with the radius, we get:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Substituting [tex]\( r = 5 \)[/tex], we get:
[tex]\[ V = \frac{4}{3} \pi (5)^3 \][/tex]
[tex]\[ V = \frac{4}{3} \pi (125) \][/tex]
[tex]\[ V = \frac{500}{3} \pi \][/tex]
Let’s address the specific steps Lara took and identify her mistakes:
1. Lara’s incorrect step was:
[tex]\[ V = \frac{4}{3} \pi (10)^3 \][/tex]
Here, Lara incorrectly used the diameter instead of the radius. She should have used the radius, which is 5.
2. The next step in Lara’s incorrect calculation was:
[tex]\[ V = \frac{4}{3} \pi (1000) \][/tex]
Lara continued with the diameter, resulting in an incorrect volume calculation.
The correct calculation should follow these steps:
[tex]\[ V = \frac{4}{3} \pi (5)^3 \][/tex]
[tex]\[ V = \frac{4}{3} \pi (125) \][/tex]
[tex]\[ V = \frac{500}{3} \pi \][/tex]
Evaluating this, we find:
[tex]\[ V \approx 523.5987755982989 \, \text{units}^3 \][/tex]
Thus, Lara’s corrected volume should be approximately [tex]\(523.5987755982989 \, \text{units}^3\)[/tex].
#### Answer to Specific Statements:
1. [tex]\( V = \frac{4}{3} \pi (1000) \)[/tex]
- No, she used the diameter instead of the radius.
2. [tex]\( V = \frac{4000}{3} \pi \, \text{units}^3 \)[/tex]
- No, her mistake was in using the diameter instead of the radius.
- She should have used the correct radius and exponent, which would have led to the correct formula: [tex]\( V = \frac{500}{3} \pi \)[/tex].
1. Lara used the formula for the volume of a sphere: [tex]\(V = \frac{4}{3} \pi r^3\)[/tex].
2. However, she used the diameter ([tex]\(d = 10\)[/tex]) directly in the formula instead of the radius ([tex]\(r\)[/tex]). The radius of a sphere is half of the diameter. So for a diameter of 10, the radius [tex]\(r = \frac{10}{2} = 5\)[/tex].
3. Rewriting the volume formula with the radius, we get:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Substituting [tex]\( r = 5 \)[/tex], we get:
[tex]\[ V = \frac{4}{3} \pi (5)^3 \][/tex]
[tex]\[ V = \frac{4}{3} \pi (125) \][/tex]
[tex]\[ V = \frac{500}{3} \pi \][/tex]
Let’s address the specific steps Lara took and identify her mistakes:
1. Lara’s incorrect step was:
[tex]\[ V = \frac{4}{3} \pi (10)^3 \][/tex]
Here, Lara incorrectly used the diameter instead of the radius. She should have used the radius, which is 5.
2. The next step in Lara’s incorrect calculation was:
[tex]\[ V = \frac{4}{3} \pi (1000) \][/tex]
Lara continued with the diameter, resulting in an incorrect volume calculation.
The correct calculation should follow these steps:
[tex]\[ V = \frac{4}{3} \pi (5)^3 \][/tex]
[tex]\[ V = \frac{4}{3} \pi (125) \][/tex]
[tex]\[ V = \frac{500}{3} \pi \][/tex]
Evaluating this, we find:
[tex]\[ V \approx 523.5987755982989 \, \text{units}^3 \][/tex]
Thus, Lara’s corrected volume should be approximately [tex]\(523.5987755982989 \, \text{units}^3\)[/tex].
#### Answer to Specific Statements:
1. [tex]\( V = \frac{4}{3} \pi (1000) \)[/tex]
- No, she used the diameter instead of the radius.
2. [tex]\( V = \frac{4000}{3} \pi \, \text{units}^3 \)[/tex]
- No, her mistake was in using the diameter instead of the radius.
- She should have used the correct radius and exponent, which would have led to the correct formula: [tex]\( V = \frac{500}{3} \pi \)[/tex].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.