Question

Math step by step answer

Answer 1

1. 432 in^2

2. 294 in^2

3. 96π in^2

4. 422 cm^2

Explanation:

1. Given:

A rectangular prism (opposite sides are equal)

l (length) = 6 in

w (width) = 8 in

h (height) = 12 in

Find: A (surface area) - ?

The surface area is the sum of the areas of all the walls

The given rectangular prism has 6 walls: 2 of each have different dimensions:

A (surface) = 6 × 12 × 2 + 8 × 12 × 2 + 6 × 8 × 2 = 432 in^2

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2. Given:

A cube (all sides and side lengths are equal)

l (length) = 7 in

Find: A (surface area) - ?

Since all sides of the cube are equal, we can find the area of one side and multiply it by the number of sides a cube has (which is 6):

A (surface) = 7 × 7 × 6 = 294 in^2

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3. Given:

A cylinder

r (radius) = 4 ft

h (height) = 8 ft

Find: A (surface area) - ?

A cylinder's surface area is the sum of the area of its 2 bases (circles) and the lateral area

`a(surface) = \pi {r}^(2) + 2\pi * r * h`

`a(surface) = 2 * \pi * {4}^(2) + 2\pi * 4 * 8 = 32\pi + 64\pi = 96\pi \: {in}^(2)`

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4. Given:

A rectangular prism (opposite sides are equal)

l (length) = 13 cm

w (width) = 7 cm

h (height) = 6 cm

Find: A (surface area) - ?

A (surface) = 13 × 7 × 2 + 6 × 7 × 2 + 13 × 6 × 2 = 422 cm^2