Prisms - GRE Quantitative Reasoning

The surface area of a rectangular prism with sides , , and is given as:

.

Two sides are known; it does not matter how they are designated, but for this problem let and , with as the unknown side. This yields equality:

Now that the three dimensions are known, it's possible to calculate the volume:

Side 1: surface area of the 6 x 7 side is 42

Side 2: surface area of the 7 x 8 side is 56

Side 3: surface area of the 6 x 8 side is 48.

We can add sides 1 and 3 to get 90, so that's not the answer.

We can add sides 1 and 1 to get 84, so that's not the answer.

We can add sides 2 and 3 to get 104, so that's not the answer.

We can add sides 2 and 2 to get 112, so that's not the answer.

This leaves the answer of 92. Any combination of the three sides of the rectangular prism will not give us 92 as the total surface area.

First, find the area of the base of the cyclinder:

and multiply that by two, since there are two sides with this measurement: .

Then, you find the width of the rectangular portion (label portion) of the prism by finding the circumference of the cylinder:

. This is then multiplied by the height of the cylinder to find the area of the rectanuglar portion of the cylinder: .

Finally, add all sides together and round: .

Find the area of the triangular sides first:

Since there are two sides of this area, we multiply the area by 2:

Next find the area of the rectangular regions. Two of them have the width of 3 feet and a length of 7 feet, while the last one has a width measurement of feet and a length of 7 feet. Multiply and add all other sides:

.

Lastly, add the triangular sides to the rectangular sides and round:

.

Remember, the formula for the volume of a rectangular prism is width times height times length:

Now, let's solve the word problem for each of these values. We know that . If length is double the width, then the length must be 6 units. If the height is two-thirds the length, then the height must be 4:

Multiply all three values together to solve for the volume:

The volume of the rectangular prism is units cubed.

The surface area of a rectangular prism with sides , , and is given as:

.

Two sides are known; it does not matter how they are designated, but for this problem let and , with as the unknown side. This yields equality:

Now that the three dimensions are known, it's possible to calculate the volume:

Side 1: surface area of the 6 x 7 side is 42

Side 2: surface area of the 7 x 8 side is 56

Side 3: surface area of the 6 x 8 side is 48.

We can add sides 1 and 3 to get 90, so that's not the answer.

We can add sides 1 and 1 to get 84, so that's not the answer.

We can add sides 2 and 3 to get 104, so that's not the answer.

We can add sides 2 and 2 to get 112, so that's not the answer.

This leaves the answer of 92. Any combination of the three sides of the rectangular prism will not give us 92 as the total surface area.

First, find the area of the base of the cyclinder:

and multiply that by two, since there are two sides with this measurement: .

Then, you find the width of the rectangular portion (label portion) of the prism by finding the circumference of the cylinder:

. This is then multiplied by the height of the cylinder to find the area of the rectanuglar portion of the cylinder: .

Finally, add all sides together and round: .

Find the area of the triangular sides first:

Since there are two sides of this area, we multiply the area by 2:

Next find the area of the rectangular regions. Two of them have the width of 3 feet and a length of 7 feet, while the last one has a width measurement of feet and a length of 7 feet. Multiply and add all other sides:

.

Lastly, add the triangular sides to the rectangular sides and round:

.

Remember, the formula for the volume of a rectangular prism is width times height times length:

Now, let's solve the word problem for each of these values. We know that . If length is double the width, then the length must be 6 units. If the height is two-thirds the length, then the height must be 4:

Multiply all three values together to solve for the volume:

The volume of the rectangular prism is units cubed.

The surface area of a rectangular prism with sides , , and is given as:

.

Two sides are known; it does not matter how they are designated, but for this problem let and , with as the unknown side. This yields equality:

Now that the three dimensions are known, it's possible to calculate the volume:

Side 1: surface area of the 6 x 7 side is 42

Side 2: surface area of the 7 x 8 side is 56

Side 3: surface area of the 6 x 8 side is 48.

We can add sides 1 and 3 to get 90, so that's not the answer.

We can add sides 1 and 1 to get 84, so that's not the answer.

We can add sides 2 and 3 to get 104, so that's not the answer.

We can add sides 2 and 2 to get 112, so that's not the answer.

This leaves the answer of 92. Any combination of the three sides of the rectangular prism will not give us 92 as the total surface area.

First, find the area of the base of the cyclinder:

and multiply that by two, since there are two sides with this measurement: .

Then, you find the width of the rectangular portion (label portion) of the prism by finding the circumference of the cylinder:

. This is then multiplied by the height of the cylinder to find the area of the rectanuglar portion of the cylinder: .

Finally, add all sides together and round: .

Find the area of the triangular sides first:

Since there are two sides of this area, we multiply the area by 2:

Next find the area of the rectangular regions. Two of them have the width of 3 feet and a length of 7 feet, while the last one has a width measurement of feet and a length of 7 feet. Multiply and add all other sides:

.

Lastly, add the triangular sides to the rectangular sides and round:

.

Remember, the formula for the volume of a rectangular prism is width times height times length:

Now, let's solve the word problem for each of these values. We know that . If length is double the width, then the length must be 6 units. If the height is two-thirds the length, then the height must be 4:

Multiply all three values together to solve for the volume:

The volume of the rectangular prism is units cubed.

The surface area of a rectangular prism with sides , , and is given as:

.

Two sides are known; it does not matter how they are designated, but for this problem let and , with as the unknown side. This yields equality:

Now that the three dimensions are known, it's possible to calculate the volume:

Side 1: surface area of the 6 x 7 side is 42

Side 2: surface area of the 7 x 8 side is 56

Side 3: surface area of the 6 x 8 side is 48.

We can add sides 1 and 3 to get 90, so that's not the answer.

We can add sides 1 and 1 to get 84, so that's not the answer.

We can add sides 2 and 3 to get 104, so that's not the answer.

We can add sides 2 and 2 to get 112, so that's not the answer.

This leaves the answer of 92. Any combination of the three sides of the rectangular prism will not give us 92 as the total surface area.

First, find the area of the base of the cyclinder:

and multiply that by two, since there are two sides with this measurement: .

Then, you find the width of the rectangular portion (label portion) of the prism by finding the circumference of the cylinder:

. This is then multiplied by the height of the cylinder to find the area of the rectanuglar portion of the cylinder: .

Finally, add all sides together and round: .

Find the area of the triangular sides first:

Since there are two sides of this area, we multiply the area by 2:

Next find the area of the rectangular regions. Two of them have the width of 3 feet and a length of 7 feet, while the last one has a width measurement of feet and a length of 7 feet. Multiply and add all other sides:

.

Lastly, add the triangular sides to the rectangular sides and round:

.

Remember, the formula for the volume of a rectangular prism is width times height times length:

Now, let's solve the word problem for each of these values. We know that . If length is double the width, then the length must be 6 units. If the height is two-thirds the length, then the height must be 4:

Multiply all three values together to solve for the volume:

The volume of the rectangular prism is units cubed.