Question

The first attempt of the basic design of a new toy is shown.
6 in
16 in
10 in
8 in
24 in
What is the surface area of the new toy to the nearest square inch?

Answer 1

The surface area of the new toy is given as follows:

1,439 in².

What is the surface area of a figure?

The surface area of a figure is given by the sum of the surface area of all it's compositions. This figure is given by a cylinder and a rectangular prism.

What is the surface area of a cylinder?

The surface area of a cylinder with radius r and height h is given by the following formula:

$S = 2\pi r(r + h)$

In this problem, the dimensions are:

r = 3 in, h = 16 in.

Hence:

$S = 2\pi \times 3(3 + 19) = 132\pi$

What is the surface area of a rectangular prism?

The surface area of a rectangular prism of length l, width w and height h is given as follows:

$S = 2(lw + lh + wh)$

In this problem, the dimensions are:

l = 24 in, h = 10 in, w = 8 in.

Hence the surface area is:

S = 2 x (24 x 10 + 24 x 8 + 10 x 8) = 1024 in²

What is the surface area of the toy?

It is the sum of the surface areas, hence:

$132\pi + 1024 = 1439 \text{in}^2$

More can be learned about the surface areas at brainly.com/question/26702574

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