Responder
1. The volume of the cylinder is approximately 73,949.75 cm³.
2. Plotting the points \( \mathrm{A}(2,2), \mathrm{B}(-2,2), \mathrm{C}(-2,-2), \) and \( \mathrm{D}(2,-2) \) on graph paper and connecting them forms a square with equal side lengths.
Solución
1. To find the volume of the cylinder, we need to know the radius of the base. Given that the circumference of the base is 176 cm, we can use the formula for the circumference of a circle to find the radius.
The formula for the circumference of a circle is:
\[ C = 2\pi r \]
Given that the circumference is 176 cm, we can set up the equation:
\[ 176 = 2\pi r \]
Solving for \( r \):
\[ r = \frac{176}{2\pi} \]
Now that we have the radius, we can find the volume of the cylinder using the formula:
\[ V = \pi r^2 h \]
Substitute the values of \( r \) and \( h \) into the formula to find the volume of the cylinder.
2. To plot the points \( \mathrm{A}(2,2), \mathrm{B}(-2,2) \mathrm{C}(-2,-2) \) and \( \mathrm{D}(2,-2) \) on graph paper and show that ABCD is a square, we can simply plot the points and connect them to form a square.
Let's calculate the volume of the cylinder first.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{176}{2\pi }\)
- step1: Reduce the fraction:
\(\frac{88}{\pi }\)
The radius of the base of the cylinder is approximately 28.01127 cm.
Now, let's calculate the volume of the cylinder using the formula \( V = \pi r^2 h \).
Calculate the value by following steps:
- step0: Calculate:
\(\pi \times 28.01127^{2}\times 30\)
- step1: Convert the expressions:
\(\pi \left(\frac{2801127}{100000}\right)^{2}\times 30\)
- step2: Multiply the numbers:
\(\frac{2801127^{2}}{100000^{2}}\times \pi \times 30\)
- step3: Multiply the terms:
\(\frac{2801127^{2}\pi }{100000^{2}}\times 30\)
- step4: Rewrite the expression:
\(\frac{2801127^{2}\pi }{100000^{2}}\times 10\times 3\)
- step5: Rewrite the expression:
\(\frac{2801127^{2}\pi }{10^{10}}\times 10\times 3\)
- step6: Reduce the numbers:
\(\frac{2801127^{2}\pi }{10^{9}}\times 3\)
- step7: Multiply:
\(\frac{2801127^{2}\pi \times 3}{10^{9}}\)
- step8: Multiply:
\(\frac{3\times 2801127^{2}\pi }{10^{9}}\)
The volume of the cylinder is approximately 73,949.75 cm³.
2. To plot the points \( \mathrm{A}(2,2), \mathrm{B}(-2,2) \mathrm{C}(-2,-2) \) and \( \mathrm{D}(2,-2) \) on graph paper and show that ABCD is a square, we can simply plot the points and connect them to form a square. The points form a square with equal side lengths.
Respondido por UpStudy AI y revisado por un tutor profesional
Explicar
Simplifique esta solución
