Question

Carla has a music box that has a base area of 9 1/2 in² and a height of 3 1/5 inches.What is the volume of the music box?

Answer 1

Given in the question:

a.) Base area of music box = 9 1/2 in²

b.) Height of music box = 3 1/5 in.

Let's recall the formula for getting the volume of a rectangular prism:

`\text{ Volume = Length x Width x Height or Base Area x Height}`

Before we plug in the values, let's first transform the mixed numbers into improper fractions.

`\text{ 9 }(1)/(2)\text{ = }\frac{1\text{ + (2 x 9)}}{2}\text{ = }\frac{1\text{ + 18}}{2}\text{ = }(19)/(2)`
`\text{ 3 }(1)/(5)\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}\text{ = }(16)/(5)`

Let's now plug in the values to get the volume of the music box.

`\text{ Volume = Base Area x Height}`
`=\text{ 9 }(1)/(2)\text{ x 3 }(1)/(5)\text{ = }(19)/(2)\text{ x }(16)/(5)\text{ = }(304)/(10)\text{ }`
`(304)/(10)\text{ = }((304)/(2))/((10)/(2))=(152)/(5)\text{ or 30 }\frac{2}{5\text{ }}in.^3`

Therefore, the volume of the music box is 30 2/5 in.^3.