Area Formula
Find the area of a rectangle with length 12 cm and width 5 cm.
60 cm²
Find the volume of a rectangular prism: l=4, w=3, h=5 cm.
60 cm³
Area = 20 cm². Scaled by k=2. New area?
80 cm²
Volume = 10 cm³. Scaled by k=2. New volume?
80 cm³
A cylindrical candle has a radius of 3 cm. You want the candle to hold exactly 135π cm³ of wax. What height does the candle need to be? Set up and solve an equation.
π(3²)h = 135π → h = 15 cm
Find the area of a triangle with base 10 in and height 7 in.
35 in²
Find the volume of a cylinder with r=3 m, h=8 m. Use π ≈ 3.14.
226.08 m³
Area = 45 in². Scaled by k=3. New area?
405 in²
Volume = 50 m³. Scaled by k=3. New volume?
1,350 m³
A rectangular prism box has a square base with side length x, and a height of 6 cm. The volume must be 384 cm³. Set up and solve an equation to find the side length of the base.
x²(6) = 384 → x² = 64 → x = 8 cm
Find the area of a circle with radius 6 m. Leave in terms of pi.
36π m²
Find the volume of a cone with r=5 ft, h=9 ft. Leave in terms of π.
75π ft³
OA = 80 m², NA = 20 m². Find k.
k = 1/2
OV = 24 ft³, NV = 192 ft³. Find k.
k = 2
A cone-shaped cup holds 48π cm³ of liquid. The height of the cup is 4 times its radius. Set up and solve an equation to find the radius and height.
(1/3)πr²(4r) = 48π → (4/3)πr³ = 48π → r³ = 36 → r ≈ 3.30 cm, h ≈ 13.20 cm
Find the area of a trapezoid with bases 8 ft and 14 ft, height 5 ft.
55 ft²
Find the volume of a sphere with r=6 in. Use π ≈ 3.14.
Find the volume of a sphere with r=6 in. Use π ≈ 3.14.
Circle: OA = 16π ft², NA = 100π ft². Find k and new radius.
k = 5/2; r = 10 ft
Sphere volumes: 27π cm³ and 125π cm³. Find k; ratio of radii?
k = 5/3; radii ratio = 5:3
A festival tent is a triangular prism. The triangular face has a height that is 3 times its base. The tent is 10 m long and must hold 240 m³ of air. Set up and solve an equation to find the base and height of the triangular face.
(1/2)(b)(3b)(10) = 240 → 15b² = 240 → b² = 16 → b = 4 m, h = 12 m
Find the area of a semicircle with diameter 20 cm. Use π ≈ 3.14.
157 cm²
Find the volume of a square pyramid with base side 8 cm, height 12 cm.
256 cm³
Areas: 12 cm² and 75 cm². Find k; original perimeter = 16 cm, find new perimeter.
k = √(75/12) = 2.5; new perimeter = 40 cm
Cone model: r=3 cm, h=5 cm. Real prop: k=4. Find volume. Leave in terms of π.
960π cm³
A sphere and a cone have the same volume. The cone has radius 6 cm and height 16 cm. Set up and solve an equation to find the radius of the sphere. Round to 2 decimal places.
(4/3)πr³ = (1/3)π(36)(16) → (4/3)r³ = 192 → r³ = 144 → r ≈ 5.24 cm