NCERT Solutions for Class 5th Maths Chapter 5 Guessing heights and depths using a reference — Let Us Estimate

Use something whose height you already know as a measuring stick. That known thing is called a reference.

The book gives you two good references on this very page.

• A single-storeyed house is about 3 m tall.
• An electric pole is about 8 m to 9 m tall.

1. Stand where you can see the whole building.
2. Count its floors. Each floor of a house is about 3 m.
3. Multiply. Floors × 3 m gives the height.
4. Check with the pole. If the building looks about as tall as one and a half electric poles, that is about 13 m — which should match your first answer roughly.

Sample answer: "The tallest building near my house is the four-storeyed hospital. Each storey is about 3 m, so 4 × 3 m = 12 m. I used a single-storeyed house as my reference, because the hospital looked exactly four of those stacked up. It also looked a little taller than the electric pole in front of it, which fits, because the pole is about 9 m."

Use the electric pole, or a person, as your reference.

1. Find a pole or a person standing near the tree.
2. See how many of them would stack up to the top of the tree. Hold your thumb up at arm's length to help you compare.
3. Multiply. If the tree is about one and a half poles high, and a pole is about 9 m, the tree is about 13 m or 14 m.

Sample answer: "The tallest tree near my home is an old neem tree in the temple courtyard. My father is about 1 m 70 cm tall, and I counted that about eight of him would reach the top. So the tree is roughly 8 × 1 m 70 cm, which is about 13 m or 14 m. I used my father's height as the reference because he was standing right at the trunk."

Depth cannot be seen, so measure it with a rope and a stone.

1. Tie a small stone to the end of a long rope.
2. Lower it slowly until the stone touches the bottom.
3. Pinch the rope at the place where it meets the top of the well.
4. Pull the rope out and measure from the stone up to your pinch, using a long tape.

For a swimming pool it is even easier: the depth is usually painted on the side, in metres, at the shallow end and the deep end.

Sample answer: "The well in our village is about 12 m deep. I tied a stone to a rope and lowered it until it touched the bottom. When I pulled the rope out and measured it with a long tape, it was 12 m. The swimming pool at the sports ground has 1 m painted at the shallow end and 2 m at the deep end."