HIM2 Unit 8: Surface Area and Volume

What is the formula for the surface area of a prism?

The surface area of a prism is calculated using the formula: SA = 2B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the prism.

What is the formula for the surface area of a cylinder?

The surface area of a cylinder is calculated using the formula: SA = 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder.

What is the formula for the surface area of a pyramid?

The surface area of a pyramid is calculated using the formula: SA = B + 1/2Pℓ, where B is the area of the base, P is the perimeter of the base, and ℓ is the slant height of the pyramid.

What is the formula for the surface area of a cone?

The surface area of a cone is calculated using the formula: SA = πr² + πrℓ, where r is the radius of the base and ℓ is the slant height of the cone.

What is the formula for the surface area of a sphere?

The surface area of a sphere is calculated using the formula: SA = 4πr², where r is the radius of the sphere.

What is the formula for the volume of a prism?

The volume of a prism is calculated using the formula: V = Bh, where B is the area of the base and h is the height of the prism.

What is the formula for the volume of a cylinder?

The volume of a cylinder is calculated using the formula: V = πr²h, where r is the radius of the base and h is the height of the cylinder.

What is the formula for the volume of a pyramid?

The volume of a pyramid is calculated using the formula: V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

What is the formula for the volume of a cone?

The volume of a cone is calculated using the formula: V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

What is the formula for the volume of a sphere?

The volume of a sphere is calculated using the formula: V = (4/3)πr³, where r is the radius of the sphere.

What is the formula for density?

The formula for density is: Density = Mass/Volume, where mass is the amount of matter in an object and volume is the space occupied by that object.

How do you calculate the density of a prism?

To calculate the density of a prism, use the formula: Density = Mass of the prism / Volume of the prism.

What is the formula for the area of a square?

The area of a square is calculated using the formula: A = s², where s is the length of one side of the square.

What is the formula for the area of a rectangle?

The area of a rectangle is calculated using the formula: A = l × w, where l is the length and w is the width of the rectangle.

What is the formula for the area of a parallelogram?

The area of a parallelogram is calculated using the formula: A = b × h, where b is the length of the base and h is the height.

What is the formula for the area of a triangle?

The area of a triangle is calculated using the formula: A = 1/2 × b × h, where b is the base length and h is the height of the triangle.

What is the formula for the area of a trapezoid?

The area of a trapezoid is calculated using the formula: A = 1/2 × (b₁ + b₂) × h, where b₁ and b₂ are the lengths of the two parallel bases and h is the height of the trapezoid.

How is a cylinder similar to a prism?

A cylinder is similar to a prism in that both have two parallel bases and a constant cross-section throughout their height.

Why do both cylinders and prisms use similar volume formulas?

Both cylinders and prisms use similar volume formulas because they both calculate volume as the area of the base multiplied by height.

How is a cone similar to a pyramid?

A cone is similar to a pyramid in that both have a single apex (vertex) and their volume can be calculated using a formula that involves the area of the base and the height.

Calculate the surface area of a rectangular box with dimensions 5 feet by 3 feet by 2 feet.

Surface area = 2lw + 2lh + 2wh = 2(5)(3) + 2(5)(2) + 2(3)(2) = 30 + 20 + 12 = 62 square feet.

Find the volume of a swimming pool with dimensions 20 feet long, 10 feet wide, and 4 feet deep.

Volume = l × w × h = 20 × 10 × 4 = 800 cubic feet.

Determine the surface area of a can of soda with a radius of 3 inches and a height of 6 inches.

Surface area = 2πr² + 2πrh = 2π(3)² + 2π(3)(6) = 18π + 36π = 54π ≈ 169.65 square inches.

Calculate the volume of a garden soil container with a radius of 1.5 feet and a height of 3 feet.

Volume = πr²h = π(1.5)²(3) = π(2.25)(3) ≈ 21.21 cubic feet.

Calculate the surface area of a pyramid-shaped tent with a square base of 4 meters and height of 3 meters.

Base area B = s² = 4² = 16 m²; Perimeter P = 4s = 4(4) = 16 m; Slant height ℓ = √((4/2)² + 3²) = √(4 + 9) = √13; Surface area SA = B + 1/2Pℓ = 16 + 1/2(16)(√13) ≈ 16 + 8√13 ≈ 54.42 m².

Find the volume of a cone with a radius of 2 inches and height of 6 inches.

Volume = (1/3)πr²h = (1/3)π(2)²(6) = (1/3)π(4)(6) = (8π) ≈ 25.13 cubic inches.

Calculate the surface area of a basketball with a radius of 12 inches.

Surface area = 4πr² = 4π(12)² = 4π(144) = 576π ≈ 1810.66 square inches.

Find the volume of a spherical water tank with a radius of 3 feet.

Volume = (4/3)πr³ = (4/3)π(3)³ = (4/3)π(27) = (36π) ≈ 113.1 cubic feet.