Geometry: Shapes and Formulas

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Questions and Answers

What is the formula for the volume of a pyramid?

V = base x height

V = 1/3 (area of base) x h (correct)

V = (base x height) / 2

V = πr²h

Which formula represents the surface area of a sphere?

S = πr² + πr²

S = 4πr² (correct)

S = 2πr²

S = πrl

What is the formula for the volume of a cone?

V = πr²h

V = (πr²)/h

V = 1/3(πrh) (correct)

V = 2/3(πr²h)

How is the area of an ellipse expressed?

A = πab Signup and view all the answers

What is the surface area of a cylinder?

S = 2πrh + πr² Signup and view all the answers

What does the symbol 'V' represent in mensuration?

Volume Signup and view all the answers

Which formula correctly represents the area of a rectangle?

A = lw Signup and view all the answers

In which type of mensuration does one calculate the perimeter of plane figures?

Plane mensuration Signup and view all the answers

What is the formula for the perimeter of a square?

P = 4s Signup and view all the answers

What does the symbol 'h' represent in mensuration?

Height perpendicular to base Signup and view all the answers

What is the formula for the area of a trapezium?

A = 1/2 ((H + h)a + bh + cH) Signup and view all the answers

Which formula represents the relationship in a right triangle?

c² = a² + b² Signup and view all the answers

How is the circumference of a circle calculated?

C = 2Πr Signup and view all the answers

What is the area of a circle with radius r?

A = Πr² Signup and view all the answers

Which expression gives the length of an arc in a circle?

L = (Πro)/180 Signup and view all the answers

What is the area formula for a trapezoid?

A = 1/2 (a + b)h Signup and view all the answers

Which formula represents the area of a triangle?

A = 1/2 bh Signup and view all the answers

What is the circumference formula for a circle?

C = Πd Signup and view all the answers

In a trapezium, which formula is used to calculate the area?

A = 1/2 [(H + h)a + bh + cH] Signup and view all the answers

What is the relationship between degrees and radians in a circle?

360 degrees = 2Π radians Signup and view all the answers

Study Notes

Pyramid

Volume formula: ( V = \frac{1}{3} \times \text{(area of base)} \times h )

Cylinder

Volume formula: ( V = \pi rh )
Surface area formula: ( S = 2\pi rh )

Ellipse

Area formula: ( A = \pi ab )

Sphere

Volume formula: ( V = \frac{4}{3}(\pi r^3) )
Surface area formula: ( S = 4\pi r^2 )

Cone

Volume formula: ( V = \frac{1}{3}(\pi rh) )
Surface area formula: ( S = \pi r \sqrt{r^2 + h^2} )

Paraboloid

Volume formula: ( V = \frac{1}{2}(\pi rh) )

Trapezoid

Area formula: ( A = \frac{1}{2}(a + b)h )

Trapezium

Area formula: ( A = \frac{1}{2}((H + h)a + bh + cH) )

Triangle

Pythagorean theorem: ( c^2 = a^2 + b^2 )
Area formula: ( A = \frac{1}{2}bh )

Circle

Area formula: ( A = \pi r^2 )
Circumference formulas: ( C = 2\pi r = \pi d )
Circular measurements: ( \pi = 180^\circ ), ( 2\pi = 360^\circ )
Arc length in degrees: ( L = \frac{\pi ro}{180} )
Arc length in radians: ( L = \pi o )

Mensuration

Branch of mathematics focusing on lengths, areas, and volumes of different shapes and solids.

Plane Mensuration

Concerned with perimeters and areas of flat figures.

Solid Mensuration

Focuses on area and volume calculations for solid shapes.

Symbols

( A ): Area
( a, b, c ): Sides of a geometric shape
( A, B, C ): Angles
( h ): Height perpendicular to the base
( L ): Length of side or edge
( r ): Radius of a circle
( d ): Diameter
( n ): Number of sides in a shape
( C ): Circumference
( V ): Volume
( S ): Surface area
( P ): Perimeter
( \pi ): Approx. value ( 3.1416 )

Quadrilateral

Square

Area formula: ( A = s^2 )
Perimeter formula: ( P = 4s )

Rhombus

Area formula: ( A = \frac{1}{2}(cd) )
Perimeter formula: ( P = 4a )

Rectangle

Area formula: ( A = lw )
Perimeter formula: ( P = 2l + 2w )

Parallelogram

Area formula: ( A = lh )
Perimeter formula: ( P = 2l + 2w )

Studying That Suits You

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Description

Test your understanding of geometric shapes and their formulas with this quiz. Covering various solids such as pyramids, cylinders, and spheres, you will evaluate your grasp on the volume and surface area calculations. Ideal for students studying geometry in middle or high school.