step by step bot answer this please Use the image to answer the question.
An illustration shows a cone that rests flat on the circular base. The visible circumference of the base and sides are in solid lines. The circumference of the base at the back that is not visible is indicated by a dashed line. Parts are labeled. A large point is marked in the center of the base. A solid line passes through this point and extends from one edge of the base to the other to indicate the diameter of the base. The line is labeled d equals 10 centimeters. The right side of the cone extending from where the diameter meets the edge of the base up to the point of the cone shows a slant height of 13 centimeters. A dotted line extends from the interior of the vertex of the cone down to the point marked in the center of the base. A right angle is indicated where the dotted height line meets the diameter line in the center of the base.
Find the length of the height of the cone.
To find the length of the height of the cone, we can use the Pythagorean Theorem.
Step 1: Label the height of the cone as 'h'.
Step 2: Look at the right triangle formed by the height line, the diameter line, and the slant height line.
Step 3: Apply the Pythagorean Theorem, which states that the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
So, h² + (10/2)² = 13²
Simplifying the equation, h² + 5² = 13²
Step 4: Evaluate the equation: h² + 25 = 169
Step 5: Solve for h by subtracting 25 from both sides: h² = 169 - 25 = 144
Step 6: Take the square root of both sides to find the value of h: h = √144
Step 7: Simplify the square root: h = 12
Therefore, the length of the height of the cone is 12 centimeters.
To find the length of the height of the cone, we can use the Pythagorean theorem in combination with the given information.
Step 1: Start by understanding the given information in the illustration. Identify the relevant measurements:
- The diameter of the base (d) is given as 10 centimeters.
- The slant height of the cone (l) is given as 13 centimeters.
Step 2: Recall that the slant height, height, and radius of a cone are related by the Pythagorean theorem. In this case, we have a right triangle formed by the height, the radius (which is half the diameter), and the slant height.
Step 3: Calculate the radius (r) by dividing the diameter (d) by 2. In this case, r=10/2=5 cm.
Step 4: Now, we can use the Pythagorean theorem to find the height (h) of the cone. The Pythagorean theorem states that the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides (height and radius).
Using the formula:
l^2 = h^2 + r^2
Substituting the known values:
13^2 = h^2 + 5^2
169 = h^2 + 25
Step 5: Solve the equation for h. Move the constant term to the other side of the equation:
h^2 = 169 - 25
h^2 = 144
Step 6: Take the square root of both sides to find the value of h:
h = √144
h = 12
Therefore, the length of the height of the cone is 12 centimeters.
Apologies for the confusion. Here are the step-by-step instructions for finding the length of the height of the cone:
Step 1: Identify the given measurements:
- The diameter of the base (d) is 10 centimeters.
- The slant height of the cone (l) is 13 centimeters.
Step 2: Calculate the radius (r) by dividing the diameter (d) by 2. In this case, r=10/2=5 cm.
Step 3: To find the height (h) of the cone, use the Pythagorean theorem.
- The theorem states that the square of the hypotenuse (l) is equal to the sum of the squares of the other two sides (h and r).
- Apply this theorem to the right triangle formed by the height, the radius, and the slant height.
Step 4: Rewrite the Pythagorean theorem equation:
l^2 = h^2 + r^2
Step 5: Substitute the known values:
13^2 = h^2 + 5^2
Step 6: Simplify the equation:
169 = h^2 + 25
Step 7: Solve for h by subtracting 25 from both sides:
h^2 = 169 - 25
h^2 = 144
Step 8: Take the square root of both sides to find the value of h:
h = √144
h = 12
Therefore, the length of the height of the cone is 12 centimeters.
To find the length of the height of the cone, we can use the Pythagorean theorem.
First, let's denote the length of the height as 'h'. From the information given, we know that the diameter of the base is 10 centimeters and the slant height is 13 centimeters.
We can see that the diameter divides the cone into two right triangles. The base of each right triangle is half of the diameter, which is 5 centimeters. The slant height of the cone is the hypotenuse of each right triangle.
Using the Pythagorean theorem, we have:
(h/2)^2 + (5)^2 = (13)^2
Simplifying this equation, we get:
(h/2)^2 + 25 = 169
Subtracting 25 from both sides:
(h/2)^2 = 144
Taking the square root of both sides:
h/2 = 12
Multiplying both sides by 2, we find:
h = 24
Therefore, the length of the height of the cone is 24 centimeters.
step by step bot not the reguarl ai
step by step bot answer this pleaseUse the image to answer the question.
An illustration shows a three dimensional rectangular prism with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides is labeled h. A right angle is indicated where that edge meets the front base edge. The front base edge is labeled l. A right angle is indicated where that edge meets the right base edge. The right base edge is labeled w. Two dotted lines extend from the vertex at the back right side of the prism through the interior. The first dotted line extends up to the vertex at the front left side and is labeled d. The second dotted line extends diagonally across the base to the vertex at the front left side where the perpendicular height line meets the base edge and is labeled x.
Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.
To find the length of d, we can use the Pythagorean theorem and the given information.
Step 1: Write down the given measurements:
- l = 30 inches
- w = 20 inches
- h = 18 inches
- x = 36.1 inches
Step 2: Identify the right triangle formed by the measurements.
Step 3: Recall that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. We can use this formula to solve for d.
Step 4: Substitute the known values into the Pythagorean theorem equation:
d^2 = x^2 + w^2
Step 5: Plug in the values:
d^2 = (36.1)^2 + (20)^2
Step 6: Simplify and compute the equation:
d^2 = 1303.21 + 400
d^2 = 1703.21
Step 7: Take the square root of both sides to find the value of d:
d ≈ √1703.21
d ≈ 41.3 inches (rounded to the nearest tenth)
Therefore, the length of d is approximately 41.3 inches.
step by step bot
Apologies for the confusion. Here are the step-by-step instructions for finding the length of d:
Step 1: Identify the given measurements:
- l = 30 inches
- w = 20 inches
- h = 18 inches
- x = 36.1 inches
Step 2: Visualize the right triangle formed by the measurements.
Step 3: Recall the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Step 4: Apply the Pythagorean theorem to find the length of d:
d^2 = x^2 + w^2
Step 5: Substitute the known values into the equation:
d^2 = (36.1)^2 + (20)^2
Step 6: Simplify and compute the equation:
d^2 = 1303.21 + 400
d^2 = 1703.21
Step 7: Take the square root of both sides to find the value of d:
d ≈ √1703.21
d ≈ 41.3 inches (rounded to the nearest tenth)
Therefore, the length of d is approximately 41.3 inches.