Question

Sunni’s bedroom has the dimensions of 11 ft by 10 ft by 10 ft. Her den has the same height but double the volume. Give two sets of the possible dimensions of the den and the volume of the den.

Answer 1

• Set 1

`Lenght=22\ ft\\\\Width=10\ ft\\\\Height=10\ ft`

• Set 2

`Lenght=11\ ft\\\\Width=20\ ft\\\\Height=10\ ft`

• The volume of the den is
  `2,200\ ft^3`

Explanation:

The volume of a rectangular prism can be calculated with this formula:

`V=lwh`

Where "l" is the lenght, "w" is the width and "h" is the height.

Knowing that Sunni’s bedroom has the dimensions of 11 feet by 10 feet by 10 feet, we can find its volume:

`V_((bedroom))=(11\ ft)(10\ ft)(10\ ft)=1,100\ ft^3`

Since her den has the same height but double the volume, we can double one dimension and keep the others the same. Then:

Set 1

`l=2(11\ ft)=22\ ft\\\\w=10\ ft\\\\h=10\ ft\\\\\\V_1=(22\ ft)(10\ ft)(10\ ft)=2,200\ ft^3`

Notice that the volume is double the volume of her bedroom.

Set 2

`l=11\ ft\\\\w=2(10\ ft)=20\ ft\\\\h=10\ ft\\\\\\V_2=(11\ ft)(20\ ft)(10\ ft)=2,200\ ft^3`

The volume is double the volume of her bedroom.

Answer 2

The volume of the bedroom is 11 x 10 x 10 = 1100 cubic feet.

The volume of the den is double, so 1100 x 2 = 2200 cubic feet.

Divide the volume of the den by the height, since it is the same as the bedroom, this will give you the area:

2200 / 10 = 220 square feet.

Two sets of numbers that could equal 220 are 22 x 10 or 22 x 11

The room can be 20 ft by 10 ft or 22 ft by 11 ft and the volume is 2200 cubic feet.