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.
(1 point)
cm
To find the length of the height of the cone, we need to use the Pythagorean Theorem. The diameter of the base is given as 10 centimeters, so the radius (which is half the diameter) is 5 centimeters.
The slant height of the cone is given as 13 centimeters. Using the Pythagorean Theorem, we can find the height of the cone:
(radius)^2 + (height)^2 = (slant height)^2
5^2 + (height)^2 = 13^2
25 + (height)^2 = 169
(height)^2 = 169 - 25
(height)^2 = 144
Taking the square root of both sides, we get:
height = √144
height = 12
Therefore, the length of the height of the cone is 12 centimeters.
Use 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.
(1 point)
in.
To find the length of d, we can use the Pythagorean Theorem.
In the given illustration, we can see that the height (h) is the vertical edge joining the front and left sides, the base length (l) is the front base edge, and the base width (w) is the right base edge.
We are given that x is the perpendicular height line, which meets the base edge at a right angle. Therefore, we can consider x as the height of a right-angled triangle.
Using the Pythagorean Theorem, we can find the length of d:
(d)^2 = (w)^2 + (x)^2
(d)^2 = (20)^2 + (36.1)^2
(d)^2 = 400 + 1303.21
(d)^2 = 1703.21
Taking the square root of both sides, we get:
d = √1703.21
d ≈ 41.3
Therefore, the length of d is approximately 41.3 inches when rounded to the nearest tenth.
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The left, front, and right faces of the pyramid and base are visible. The back face is not visible, but its position is indicated by a dashed line. The back base edge is not visible, but its position is indicated by a dashed line. The left base edge is labeled a. The back left lateral edge is labeled e. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge and is labeled r. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. The dotted slant height line is labeled s.
For the square pyramid, the lateral edge length, e, is 25 in., and the slant height, s, is 24 in. Find the height of the pyramid, h. Round the answer to the nearest whole number. Hint: Before finding the length of h, you will first need to find the length of r
.
(1 point)
The height of the square pyramid is
in.
To find the height of the square pyramid, we first need to find the length of r.
In the given illustration, we can see that the lateral edge length (e) is labeled as 25 inches and the slant height (s) is labeled as 24 inches.
Using the information given, we can find the length of r by using the Pythagorean Theorem.
(r)^2 = (e)^2 - (s)^2
(r)^2 = (25)^2 - (24)^2
(r)^2 = 625 - 576
(r)^2 = 49
Taking the square root of both sides, we get:
r = √49
r = 7 inches.
Now that we have the length of r, we can find the height (h) of the pyramid.
From the illustration, we can see that the height line (h) and the slant height line (s) form a right triangle.
Using the Pythagorean Theorem again, we can find the length of h:
(h)^2 = (s)^2 - (r)^2
(h)^2 = (24)^2 - (7)^2
(h)^2 = 576 - 49
(h)^2 = 527
Taking the square root of both sides, we get:
h = √527
h ≈ 22.9
Therefore, the height of the square pyramid is approximately 23 inches when rounded to the nearest whole number.
Use the image to answer the question.
A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point)
ft.
To find the length of the edge of the square base, we can use the Pythagorean Theorem.
In the given illustration, we are given that the height of the pyramid is 321 feet and the slant height is 436.5 feet.
Let's represent the length of the edge of the square base as "l".
Using the Pythagorean Theorem, we can find the length of l:
(l/2)^2 + (321)^2 = (436.5)^2
(l/2)^2 + 103041 = 190771.25
(l/2)^2 = 190771.25 - 103041
(l/2)^2 = 87730.25
Multiplying both sides by 4, we get:
l^2 = 350921
Taking the square root of both sides, we get:
l = √350921
l ≈ 592.1
Therefore, the length of the edge of the square base is approximately 592.1 feet when rounded to the nearest tenth.