Geometric Formulas as Literal Equations - Examples
Read this topicExplanations 4
- Geometric formulas are used to help figure out things about the geometry of shapes and objects. When we say "geometry," we mean things like length, width, radius, circumference,…
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Joshua Siktar, Jonathan Heller, Anusha Rahman
- Literal equations appear everywhere in geometry. Equations describe relationships between different geometric objects, such as angles, volumes, and side lengths. We call them li…
By Joshua Siktar, Jonathan Heller, Anusha Rahman
- One of the most famous literal equations is the Pythagorean theorem: In words, this states that in a right triangle, the sum of the squares of the lengths of the legs equals the…
By Joshua Siktar
- (Video) Literal Equations - Area Formula by Brian McLogan This video by Brian McLogan explains how to solve for bbb in the area of a triangle formula. This video uses the area f…
By Anusha Rahman
Problems 40
- Solve for the radius of a sphere, rrr, in terms of the volume, VVV. V=43 πr3V=\frac{4}{3}\ \pi r^3V=34 πr3
- Find a formula for the base bbb of a triangle, in terms of the height hhh and area AAA of the triangle.
- The equation for a line is y=mx+by=mx+by=mx+b. Solve for mmm when xxx is nonzero.
- The Pythagorean theorem is given by: a2+b2=c2a^2+b^2=c^2a2+b2=c2. Solve for aaa.
- The volume of a can is equal to the area of the bottom multiplied by the height of the can. What kind of function is the volume function V(r)V(r)V(r) of the can in terms of the …
- The diameter of the moon is 215921592159 miles. The volume of Earth is about 49.349.349.3 times larger than that of the moon. What is the Earth's diameter, approximately?
- If a rectangle has a length of 2a2a2a and a width of 3a+43a + 43a+4, what is the area of the rectangle?
- Which of these describes the formula for the perimeter PPP of a rectangle, if LLL represents length and WWW represents width?
- If a rectangle has side lengths of 3x+23x + 23x+2 and 3x−23x - 23x−2, what is the area of this rectangle?
- If a rectangle has an area of 16x4−916x^4 - 916x4−9, where x=2018x = 2018x=2018, what are its possible dimensions?
- The volume of a circular cone is V=13(π)r2hV=\frac{1}{3}(\pi)r^2hV=31(π)r2h. Solve for hhh.
- Given the formula for a triangle's height in terms of its area and base, solve for AAA in terms of bbb and hhh: 2Ab=h\frac{2A}{b}=hb2A=h
- The diameter, ddd, is twice the radius, rrr. If possible, express ddd as a function of CCC.
- The formula for the surface area of a cylinder is A=2(π)rh+2(π)r2A=2(\pi)rh+2(\pi)r^2A=2(π)rh+2(π)r2 Which of the symbols contained within are variables? Select all that apply.
- Isolate sss as a function of AAA.
- The volume of a cube with side length sss is V=s3V=s^3V=s3. Isolate sss in terms of VVV.
- Isolate π\piπ in the following equation. C=dπC=d\piC=dπ
- Isolate hhh, the height of a cylinder, in the formula for its volume: V=hπr2V=h\pi r^2V=hπr2
- Isolate the radius rrr of a circle from its diameter ddd: d=2rd=2rd=2r
- Select the variables in the equation. C=2πrC=2\pi rC=2πr
- The radius of a circle is the square root of the area over π.\pi.π. Write this relationship as a literal equation in which rrr is isolated on one side.
- Write an equation for TTT, the total area of a circle and a square where the radius rrr is the same length as the side of the square.
- Write an equation for the area of a square that has a circle inscribed in it with a radius rrr.
- The length and width of some rectangular frame is lll feet and www feet respectively. If we double both the length and width, how much would the area increase by?
- τ\tauτ is defined to be twice of π\piπ. We know the circumference of a circle with radius rrr is 2πr2\pi r2πr. Write the circumference in terms of τ\tauτ instead of π\piπ.
- τ\tauτ is defined to be twice of π\piπ. We know the area of a circle with radius rrr is πr2\pi r^2πr2. Write the area in terms of τ\tauτ instead of π\piπ.
- Fanny is making some paper cubes with side length of lll inches. How much paper does she need if she wants to make 202020 of these cubes?
- Georgia is purchasing a table cover for her picnic table. Let's say her picnic table has dimensions lll inches by www inches. Georgia wants the dimensions of the cover to be 333…
- The volume of a cylinder with a radius of rrr and a height of hhh is expressed as the following: V=πr2hV=\pi r^2 hV=πr2h What is the volume of a cylinder with a radius of 555 an…
- The volume of a cylinder with a radius of rrr and a height of hhh is expressed as the following: V=πr2hV=\pi r^2 hV=πr2h Say we have a separate cylinder with a radius twice of t…
- A triangle has base and height of aaa and bbb, respectively. Coincidentally, a rectangle has width and length of aaa and bbb, respectively. \\ What is the difference between the…
- The volume of a right rectangular pyramids is V=lwh3V=\frac{lwh}{3}V=3lwh, where lll and www are the dimensions of the base and hhh is the height.\\ Write the expression for ww…
- Lee is gift wrapping some cubic boxes. They are the same size and have side length lll inches. How much wrapping paper would Lee need if he is wrapping 121212 of these boxes?
- An empty swimming pool is 303030 feet wide and 505050 feet long. Water is being pumped into the pool at a constant speed and the level raises 111 feet every half an hour. What i…
- The area of a trapezoid is: A=12(a+b)×hA = \frac{1}{2} (a+b)\times hA=21(a+b)×h Where hhh is the height and a,ba, ba,b are the two bases. Can you write a formula of hhh in term…
- Two triangles have the same base, but the height of one triangle is 444 units longer than the other. What is the difference between the areas of these two triangles?
- A giant apple pie baked for a farm festival has a radius of 333 feet. What is the difference of area in each slice if we cut the pie into 888 slices versus 101010 slices?
- The volume of a circular cone with radius rrr and height hhh is given by the following formula: 13×π×r2×h\frac{1}{3}\times \pi \times r^2 \times h31×π×r2×h If we have 111 cubic…
- Recall the circumference of of a circle given its diameter ddd is C=πdC = \pi dC=πd. The diameter of a circle is twice of its radius. What is rrr in terms of ddd? What is CCC in…
- If a backyard has length, l=3x+2l=3x+2l=3x+2 and width, w=9xw=9xw=9x, what is the area of the backyard in terms of xxx?