# Whose room is bigger?

Tanya and Tinku are good friends.  No, they are extremely close buddies.  Yet, they act as rivals even for silly things.  Today, Tinku says that his room is bigger than Tanya’s room.  Mind you, they live in their own houses. One might say,” Who cares?” but no, they had to settle the matter.  So Tinku asked his mom for a measuring tape. They started with Tinku’s room.

# Measurements – lengths, areas and volumes

Tinku had a big room with windows on one wall and the door on the other. The room also had a large bed and a desk in it.  Never mind.  They moved the bed, the desk and whatever they needed to in order to do the measurements.  The floor of the room was rectangular – 4 meters long and 3 meters wide. So they calculated that the area of the room to be 4 x 3 which comes to 12 square meters. Tinku climbed on his desk and then they measured that the height of the room. It was 2.5 meters.  So the room was 4 meters long, 3 meters wide and 2.5 meters high.  That gave them the volume of the room which was area x height which was 12 x 2.5 or 30 cubic meters  You could also say 4 x 3 x 2.5 which again comes out to 30 cubic meters.

Then they came over to Tanya’s house and Tinku took the measuring tape with him.  When they started to measure, Tanya’s mom came and asked them what they were doing.  She heard their arguments but left the two headstrong kids alone.   Tanya’s floor was square shaped with each wall being 3.5 meters So the floor area comes to 3.5 x 3.5 or 12.25 square meters.

Tanya: See the area of my room is 12.25 square meters.  Your room is only 12 square meters.  So my room is bigger than yours.

Tinku: Not so fast, we still have to measure the height of your room.

Even though the height did not look different from Tinku’s room, they measured it.

Tinku:  The height of your room is a little less than my room. Yours is only 2.45 meters high while mine is 2.5 meters.

Tanya: I calculated that the volume of my room is 12.25 x 2.45 which is 30.0125 cubic meters. It is bigger than your room which is only 30 cubic meters.

Tinku: They are about the same plus my roof has an extra layer of good paint.

Would their rivalry ever end?

# Challenge

Tinku’s mom has a bucket with 10 liters of water in it.  Tinku wants the bucket and tells mom that he will pour the water into a plastic container which is 50 cm long, 40 cm long and 30 cm high.  Mother agrees but tells him not to spill any water. Do you think it will work?  Remember 1000 liters equals 1 cubic meter.

Solution:  The plastic container is 50 cm long, 40 cm wide and 30 cm high. This is the same as saying that the container is 0.50 meters long, 0.40 meters wide and 0.30 cm meters.  The volume of the container is 0.06 cubic meters which is the same as 1000 x 0.06 or 60 liters. Obviously, the container is big enough to hold the 10 liter water in the bucket.

You could also do it this way. The volume of the plastic container is 50 cm x 40 cm x 30 cm.  This comes out to 60,000 cubic centimeters.  One cubic centimeter is the same as 1 milliliter.  The volume can be written as 60,000 ml or 60 liters  You get the same answer.