A scale drawing uses a scale of 1 cm : 5 m. A wall is 8 cm long in the drawing. What is the actual length? — 40 m.8 cm × 5 = 40 m. Multiply drawing length by the scale factor.
What does the scale 1 : 100 mean? — Every 1 unit in the drawing equals 100 units in reality.A scale of 1:100 means every 1 unit in the drawing represents 100 units in actual size.
A map has a scale of 1 in = 25 miles. Two cities are 3 inches apart on the map. What is the actual distance? — 75 miles.3 × 25 = 75 miles. Multiply map distance by scale factor.
A floor plan is drawn at a scale of 1 cm : 4 m. If a room is 3 cm × 5 cm on the plan, what are the actual dimensions? — 12 m × 20 m.3 cm × 4 = 12 m; 5 cm × 4 = 20 m. Actual room is 12 m × 20 m.
A scale drawing uses the scale 2 cm : 1 km. How many cm on the drawing represent 5 km? — 10 cm.5 km × (2 cm / 1 km) = 10 cm on the drawing.
On a blueprint, 1 inch represents 8 feet. A hallway is 3.5 inches on the blueprint. How long is the actual hallway? — 28 ft.3.5 × 8 = 28 feet. Multiply blueprint length by scale factor.
Which of these is NOT a valid way to write a scale? — 50%.Percentages express ratios differently and are not a valid scale format for drawings. Scales use ratios, fractions, or measurement equivalences.
What is the formula for the circumference of a circle? — C = 2πr.Circumference C = 2πr (or equivalently C = πd since d = 2r).
What is the formula for the area of a circle? — A = πr².Area A = πr². Remember: area uses r squared, circumference uses r to the first power.
A circle has a radius of 6 cm. What is its diameter? — 12 cm.Diameter = 2 × radius = 2 × 6 = 12 cm.
A circle has a diameter of 10 in. What is its radius? — 5 in.Radius = diameter ÷ 2 = 10 ÷ 2 = 5 in.
What is the circumference of a circle with radius 7? Leave in terms of π. — 14π.C = 2πr = 2π(7) = 14π.
What is the area of a circle with radius 3 cm? Leave in terms of π. — 9π cm².A = πr² = π(3²) = 9π cm².
What value is π approximately equal to? — 3.14.π ≈ 3.14159... The common approximation is 3.14 or the fraction 22/7.
A circular label has a radius of 4 cm. What is the area? Use π ≈ 3.14. — 50.24 cm².A = πr² = 3.14 × 16 = 50.24 cm².
A circle has diameter 20 m. What is its circumference? Leave in terms of π. — 20π m.C = πd = π(20) = 20π m.
Two angles that sum to 90° are called: — Complementary.Complementary angles sum to 90°. Remember: C for Complementary, C for Corner (right angle = 90°).
Two angles that sum to 180° are called: — Supplementary.Supplementary angles sum to 180°. They form a straight line together.
Vertical angles are: — Always equal.Vertical angles are formed opposite each other when two lines intersect. They are always equal in measure.
An angle measures 55°. What is the measure of its complement? — 35°.90° − 55° = 35°. Complementary angles sum to 90°.
An angle measures 110°. What is the measure of its supplement? — 70°.180° − 110° = 70°. Supplementary angles sum to 180°.
Two lines intersect. One angle is 45°. What is the measure of the angle vertically opposite to it? — 45°.Vertical angles are equal. The angle vertically opposite to 45° is also 45°.
An angle measures 27°. What is the measure of its complement? — 63°.90° − 27° = 63°.
The sum of the interior angles of any triangle is: — 180°.The interior angles of any triangle always sum to exactly 180°, regardless of the triangle's shape or size.
The sum of the interior angles of any quadrilateral is: — 360°.Quadrilaterals have 4 sides. The interior angles always sum to 360°.
A triangle has angles of 60° and 80°. What is the third angle? — 40°.180° − 60° − 80° = 40°.
A triangle has two equal angles of 55° each. What is the third angle? — 70°.180° − 55° − 55° = 70°.
Which set of angles could form a triangle? — 60°, 60°, 60°.60+60+60 = 180° ✓. The others don't sum to 180°.
A quadrilateral has angles of 85°, 100°, and 95°. What is the fourth angle? — 80°.360° − 85° − 100° − 95° = 80°.
What type of triangle has one angle greater than 90°? — Obtuse.An obtuse triangle has one angle greater than 90°. The other two angles must be acute to keep the total at 180°.
A triangle with all equal angles is called: — Equilateral.An equilateral triangle has all three sides and all three angles equal (each = 60°).
A triangle with two equal sides is called: — Isosceles.An isosceles triangle has exactly two equal sides (and the base angles opposite those sides are also equal).
Surface area is measured in what type of units? — Square units.Surface area is a 2D measurement (area of flat faces), so it is measured in square units (cm², m², in²).
Volume is measured in what type of units? — Cubic units.Volume measures 3D space, so it uses cubic units (cm³, m³, in³).
What is the volume of a rectangular prism with length 4, width 3, and height 2? — 24.V = l × w × h = 4 × 3 × 2 = 24 cubic units.
A cube has side length 5 cm. What is its volume? — 125 cm³.V = s³ = 5³ = 125 cm³.
How many faces does a rectangular prism have? — 6.A rectangular prism has 6 faces: top, bottom, front, back, left, and right.
The volume of a pyramid is what fraction of the volume of a prism with the same base and height? — 1/3.V_pyramid = (1/3) × B × h. A pyramid holds exactly 1/3 the volume of a prism with the same base and height.
The surface area of a rectangular prism includes which faces? — All 6 rectangular faces.Surface area is the total of ALL 6 faces: top, bottom, front, back, left, and right.
A pyramid has 1/3 the volume of a prism with the same base and height. If the prism volume is 90 cm³, what is the pyramid volume? — 30 cm³.V_pyramid = (1/3)(90) = 30 cm³.
A rectangular prism is 3 m × 2 m × 5 m. What is its volume in cubic meters? — 30 m³.V = 3 × 2 × 5 = 30 m³.
What is a cross section? — The 2D shape revealed when a flat cut is made through a 3D solid.A cross section is the 2D shape you see when a flat plane cuts through a 3D solid.
If you slice a sphere through its center, what shape is the cross section? — A circle.Any flat cut through a sphere produces a circle. A cut through the center produces the largest circle (great circle).
What cross section do you get if you slice a cylinder horizontally (parallel to the base)? — Circle.Slicing a cylinder horizontally (parallel to the base) produces a circle, since you're cutting through the circular cross-section.
What cross section do you get if you slice a cylinder vertically (perpendicular to the base, along the axis)? — Rectangle.A vertical cut along a cylinder's axis produces a rectangle with width equal to the diameter and height equal to the cylinder height.
What cross section do you get if you slice a cone horizontally (parallel to the base)? — Circle.A horizontal cut through a cone (parallel to the base) produces a smaller circle.
What cross section do you get if you slice a cone vertically through its apex? — Triangle.A vertical cut through the apex of a cone produces a triangle (isosceles).
A horizontal cross section of a pyramid gets larger as you cut closer to: — The base (bottom).The pyramid narrows toward the apex. Cuts closer to the base produce larger cross sections; cuts near the apex produce smaller ones.
An architect slices a conical roof section to check its dimensions. A horizontal cut produces what shape? — Circle.Horizontal cross sections of cones are always circles.