what is the volume of the composite space figure to the nearest whole number 216
Space Figures and Basic Solids
Space figures and basic solids
Space figures
Cantankerous-section
Volume
Surface area
Cube
Cylinder
Sphere
Cone
Pyramid
Tetrahedron
Prism
Infinite Figure
A space effigy or 3-dimensional figure is a figure that has depth in addition to width and height. Everyday objects such as a tennis brawl, a box, a bicycle, and a redwood tree are all examples of space figures. Some common simple infinite figures include cubes, spheres, cylinders, prisms, cones, and pyramids. A space figure having all flat faces is called a polyhedron. A cube and a pyramid are both polyhedrons; a sphere, cylinder, and cone are not.
Cantankerous-Section
A cantankerous-section of a infinite figure is the shape of a item two-dimensional "piece" of a space effigy.
Example:
The circle on the right is a cross-section of the cylinder on the left.
The triangle on the right is a cross-section of the cube on the left.
Volume
Volume is a measure out of how much space a space figure takes up. Volume is used to measure a space figure just equally surface area is used to mensurate a plane figure. The volume of a cube is the cube of the length of one of its sides. The volume of a box is the production of its length, width, and tiptop.
Example:
What is the volume of a cube with side-length vi cm?
The book of a cube is the cube of its side-length, which is 6 three = 216 cubic cm.
Instance:
What is the volume of a box whose length is 4cm, width is 5 cm, and height is 6 cm?
The book of a box is the product of its length, width, and height, which is four × 5 × half-dozen = 120 cubic cm.
Surface Surface area
The surface area of a infinite figure is the total area of all the faces of the figure.
Case:
What is the surface area of a box whose length is 8, width is 3, and height is four? This box has half-dozen faces: ii rectangular faces are viii by 4, ii rectangular faces are 4 by 3, and 2 rectangular faces are 8 past three. Calculation the areas of all these faces, nosotros go the surface area of the box:
8 × 4 + viii × 4 + four × three + 4 × 3 + 8 × 3 + 8 × three =
32 + 32 + 12 + 12 +24 + 24=
136.
Cube
A cube is a three-dimensional figure having 6 matching square sides. If L is the length of one of its sides, the volume of the cube is L 3 = 50 × 50 × 50 . A cube has vi square-shaped sides. The surface expanse of a cube is six times the area of one of these sides.
Example:
The space figure pictured beneath is a cube. The grayed lines are edges hidden from view.
Example:
What is the volume and surface are of a cube having a side-length of 2.1 cm?
Its book would exist ii.1 × 2.ane × 2.i = 9.261 cubic centimeters.
Its surface area would be half dozen × 2.1 × two.i = 26.46 square centimeters.
Cylinder
A cylinder is a infinite figure having two congruent round bases that are parallel. If L is the length of a cylinder, and r is the radius of one of the bases of a cylinder, then the volume of the cylinder is Fifty × pi × r 2 , and the surface expanse is 2 × r × pi × L + 2 × pi × r 2 .
Example:
The figure pictured below is a cylinder. The grayed lines are edges hidden from view.
Sphere
A sphere is a space effigy having all of its points the aforementioned distance from its center. The distance from the eye to the surface of the sphere is called its radius. Any cantankerous-section of a sphere is a circle.
If r is the radius of a sphere, the volume V of the sphere is given by the formula V = iv/iii × pi × r 3 .
The surface expanse S of the sphere is given by the formula S = iv × pi × r two .
Example:
The space figure pictured below is a sphere.
Example:
To the nearest tenth, what is the volume and expanse of a sphere having a radius of 4cm?
Using an estimate of 3.fourteen for pi ,
the volume would be 4/3 × iii.14 × 4 3 = 4/3 × 3.fourteen × iv × iv × 4 = 268 cubic centimeters.
Using an estimate of 3.14 for pi , the surface expanse would exist 4 × 3.14 × 4 2 = 4 × 3.xiv × 4 × 4 = 201 square centimeters.
Cone
A cone is a space figure having a circular base and a unmarried vertex.
If r is the radius of the round base, and h is the tiptop of the cone, and so the volume of the cone is i/3 × pi × r 2 × h .
Example:
What is the book in cubic cm of a cone whose base has a radius of 3 cm, and whose peak is 6 cm, to the nearest 10th?
We will utilise an estimate of 3.fourteen for pi .
The volume is one/3 × pi × iii 2 × half dozen = pi ×18 = 56.52, which equals 56.5 cubic cm when rounded to the nearest 10th.
Example:
The pictures beneath are two different views of a cone.
Pyramid
A pyramid is a space effigy with a square base and iv triangle-shaped sides.
Example:
The moving-picture show beneath is a pyramid. The grayed lines are edges hidden from view.
Tetrahedron
A tetrahedron is a four-sided space effigy. Each face of a tetrahedron is a triangle.
Instance:
The picture show below is a tetrahedron. The grayed lines are edges subconscious from view.
Prism
A prism is a space figure with ii congruent, parallel bases that are polygons.
Examples:
The effigy below is a pentagonal prism (the bases are pentagons). The grayed lines are edges hidden from view.
The effigy below is a triangular prism (the bases are triangles). The grayed lines are edges hidden from view.
The figure beneath is a hexagonal prism (the bases are hexagons). The grayed lines are edges hidden from view..
Source: https://mathleague.com/index.php/about-the-math-league/mathreference?id=79
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