An igloo approximates a hemisphere, with

Question

An igloo approximates a hemisphere, with

an entrance tunnel that approximates half
a right cylinder.
The base of the igloo has diameter 4.0 m. The
entrance is 0.8 m long; it has an external radius
of 0.8 m and an internal radius of 0.7 m.
Calculate the surface area of the outside of the
igloo and tunnel.

Answer 1

SA of hemisphere + SA of half lateral cylinder - area semi circle(inner radius) = 8pi + .64pi - .245pi = 8.395pi

Answer 2

To calculate the surface area of the outside of the igloo and tunnel, we need to find the surface area of each component separately and then add them together.

Let's start by finding the surface area of the igloo. Since the igloo approximates a hemisphere, the surface area of a hemisphere is given by the formula:

A = 2πr^2

where A is the surface area and r is the radius.

Since the given information provides the diameter of the base, we first need to find the radius of the base. The diameter is 4.0 m, so the radius (r) is half of that:

r = 4.0 m / 2 = 2.0 m

Now, we can find the surface area of the igloo:

A_igloo = 2πr^2
= 2π(2.0 m)^2
= 8π m^2

Next, let's find the surface area of the tunnel. The tunnel can be thought of as a cylinder. The surface area of a cylinder is given by the formula:

A = 2πrh

where A is the surface area, r is the radius, and h is the height.

We are given the external radius of the tunnel (0.8 m), but we need to find the height. From the given information, we know that the entrance is 0.8 m long, which means the height of the tunnel is also 0.8 m.

Now, we can find the surface area of the tunnel:

A_tunnel = 2πrh
= 2π(0.8 m)(0.8 m)
= 1.28π m^2

Finally, we can calculate the total surface area of the outside of the igloo and tunnel by adding the surface areas of the igloo and tunnel together:

Total surface area = A_igloo + A_tunnel
= 8π m^2 + 1.28π m^2
= 9.28π m^2

Therefore, the surface area of the outside of the igloo and tunnel is approximately 9.28π square meters.

Answer 3