use euler's formula to find the missing number
vertices 23
edges 39 faces ?
Euler's formula states that the number of vertices plus the number of faces minus the number of edges equals 2.
We are given the number of vertices (23) and edges (39), so we can plug these into the formula and solve for the missing number (faces):
23 + F - 39 = 2
F - 16 = 2
F = 18
Therefore, the missing number is 18.
what is the lateral area of the rectangular prism? round your answer to the nearest whole number asume 3m*5m rectangles on the left and right are the bases and 14m is the hight
The lateral area of a rectangular prism is the sum of the areas of its lateral faces, which are the faces that are not bases (top and bottom).
In this case, there are four lateral faces: two 3m x 14m faces on the front and back, and two 5m x 14m faces on the left and right.
The area of one of the 3m x 14m faces is:
3m x 14m = 42 m^2
The area of one of the 5m x 14m faces is:
5m x 14m = 70 m^2
So the total lateral area is:
2(42 m^2) + 2(70 m^2) = 224 m^2
Rounded to the nearest whole number, the lateral area of the rectangular prism is 224 square meters.
what is the surface area of the cylinder in terms of Pi the diagram is not drawn to scale
6 in. radius
24 in. high
The surface area of a cylinder can be calculated by adding the area of the top and bottom circles (which have a radius of 6 inches in this case) to the area of the lateral surface (which is a rectangle that can be "unwrapped" from the cylinder and has a height of 24 inches and a width equal to the circumference of the circle, which is 2πr).
Area of top and bottom circles = 2πr^2 = 2π(6 in.)^2 = 72π in.^2
Circumference of circle = 2πr = 2π(6 in.) = 12π in.
Area of lateral surface = width x height = (12π in.) x (24 in.) = 288π in.^2
Total surface area = area of circles + area of lateral surface = 72π in.^2 + 288π in.^2 = 360π in.^2
Therefore, the surface area of the cylinder in terms of Pi is 360π square inches.
what is the lateral area of a rectangular pentagonal pyramid that has a slant height of18 in. and a base side length of 9 in
To find the lateral area of a rectangular pentagonal pyramid, we need to add up the areas of the five triangular faces.
Each of the triangular faces is an isosceles triangle with one leg being the slant height of 18 in, and the other two legs equal to half the diagonal of the rectangular base.
The diagonal of a rectangle with side lengths of 9 in. is found using the Pythagorean theorem:
d^2 = 9^2 + 9^2 = 81 + 81 = 162
d = √162 = 9√2
Half of the diagonal (length of one of the legs of the isosceles triangle) is:
(1/2)*9√2 = (9/2)√2
Now we can find the area of one of the triangular faces using the formula for the area of a triangle:
A = (1/2) * base * height
The base of the triangle is one of the edges of the pentagonal base, which is 9 inches.
The height of the triangle is the slant height, which is 18 inches.
Therefore, the area of one of the triangular faces is:
(1/2)*9*(9/2)√2*(18) = 81√2 in^2
Since there are five triangular faces, we can find the lateral area of the pyramid by multiplying the area of one of the triangles by 5:
Lateral area = 5 * 81√2 in^2 = 405√2 ~ 573.2 in^2 (rounded to one decimal place)
Therefore, the lateral area of the rectangular pentagonal pyramid is approximately 573.2 square inches.
what is the lateral area of the cone to the nearest whole number the figure is not drawn to scale 50 M 240 m radius
To find the lateral area of a cone, we can use the formula:
Lateral area = πrℓ
where r is the radius of the circular base and ℓ is the slant height.
In this case, the radius is 240 m and the slant height is 50 m.
We can find the lateral area by plugging these values into the formula and simplifying:
Lateral area = π(240 m)(50 m) = 12,000π m²
Rounding to the nearest whole number, the lateral area of the cone is:
Lateral area ≈ 37,699 m²
Therefore, the lateral area of the cone to the nearest whole number is 37,699 square meters.
what is the maximum volume of a pyramid that can fit inside a cube with side length of 18 cm
what is the volume of a square pyramid with base edges of 18 cm and slant height of 15 cm
what is the volume of a the cone rounded to the nearest tenth to diagram is not drawn to scale the height of the cone is 15 yd
the volume of a sphere is 4000 Pi M cubed what is the surface area of the sphere to the nearest square meter