Question

NO LINKS! URGENT HELP PLEASE!

Solve for the surface area. Leave answers exact. ​

Answer 1

a) 396 cm²

c) 132π km²

Explanation:

Part a

The formula for the surface area of a rectangular prism is:

`\boxed{\begin{minipage}{5.5cm}\underline{Surface area of a rectangular prism}\\\\$SA=2(wl+hl+hw)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width.\\\phantom{ww}$\bullet$ $l$ is the length.\\\phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`

From inspection of the given diagram:

• w = 6 cm
• l = 7 cm
• h = 12 cm

Substitute the values of w, l and h into the formula:

`\begin{aligned}\textsf{Surface area}&=2(6 \cdot 7+12 \cdot 7+12 \cdot 6)\\&=2(42+84+72)\\&=2(198)\\&=396\; \sf cm^2\end{aligned}`

Therefore, the surface area of the given rectangular prism is 396 cm².

`\hrulefill`

Part c

The formula for the surface area of a cylinder is:

`\boxed{\begin{minipage}{6.5cm}\underline{Surface area of a cylinder}\\\\$SA=2\pi rh+2\pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\\phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`

From inspection of the given diagram:

• r = 6 km
• h = 5 km

Substitute the values of r and h into the formula:

`\begin{aligned}\textsf{Surface area}&=2 \pi (6)(5)+2 \pi (6)^2\\&=2 \pi (30)+2 \pi (36)\\&=60 \pi+72 \pi\\&=132 \pi \; \sf km^2\end{aligned}`

Therefore, the surface area of the given rectangular prism is 132π km².

Answer 2

a. 396cm².

b. 414.69 km²

Explanation:

a.

The surface area of a cuboid is the total area of all the faces of the cuboid. A cuboid is a six-sided object with each face being a rectangle. The formula for the surface area of a cuboid is:

Surface area = 2lw + 2lh + 2wh=2(lw+lh+wh)

where:

• l = length of the cuboid
• w = width of the cuboid
• h = height of the cuboid

Here, l=7cm, w=6cm and h=12 cm

substituting value:

Surface area : 2(7*6+7*12+6*12)=396 cm²

Therefore, Surface area is 396cm².

b.

The surface area of a cylinder is the total area of all the faces of the cylinder. It can be calculated using the following formula:

Surface area = 2πr² + 2πrh=2πr(r+h)

Where:

• r is the radius of the cylinder
• h is the height of the cylinder

In this case, we have:

r = 6 km

h = 5 km

Therefore, the surface area of the cylinder is:

Surface area =2π*6(6+5)=132π or 414.69 km²

Therefore, the surface area of the cylinder is approximately 414.69square kilometers.