Maharashtra Board Class 8 Maths Chapter 16 Surface Area and Volume Set 16.1 Solutions

Question 1. Find the volume of a box if its length, breadth and height are 20 cm, 10.5 cm and 8 cm respectively. Given: For cuboid shaped box,
length \( (l) = 20 \text{ cm}\), breadth \( (b) = 10.5 \text{ cm}\) and height \( (h) = 8\text{cm}\)
To find: Volume of a box
Solution:
Volume of a box \( = l \times b \times h\)
\( = 20 \times 10.5 \times 8\)
\( = 1680 \text{ cc}\)
\(\therefore\) The volume of the box is \(1680 \text{ cc}\).
Answer: The volume of the box is \(1680 \text{ cc}\).
In simple words: To find the volume of a cuboid, multiply its length, breadth, and height. For the given dimensions, the product is 1680 cubic centimeters.

🎯 Exam Tip: Always ensure units are consistent before calculating volume. If different units are given, convert them to a common unit first.

Question 2. A cuboid shaped soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm. Given: For cuboid shaped soap bar,
length \( (l) = 10 \text{ cm}\), breadth \( (b) = 5 \text{ cm}\) and volume \( = 150 \text{ cc}\)
To find: Thickness of the soap bar \( (h)\)
Solution:
Volume of soap bar \( = l \times b \times h\)
\(\therefore 150 = 10 \times 5 \times h\)
\(\therefore 150 = 50h\)
\(\frac{150}{50} = h\)
\(\therefore 3 = h\)
\(i.e., h = 3 \text{ cm}\)
\(\therefore\) The thickness of the soap bar is \(3 \text{ cm}\).
Answer: The thickness of the soap bar is \(3 \text{ cm}\).
In simple words: Given the volume, length, and breadth of a cuboid, you can find the height (thickness) by dividing the volume by the product of the length and breadth. Here, 150 divided by (10 times 5) gives a thickness of 3 cm.

🎯 Exam Tip: When given volume and two dimensions, use the volume formula to solve for the missing dimension by rearranging the equation.

Question 3. How many bricks of length 25 cm, breadth 15 cm and height 10 cm are required to build a wall of length 6 m, height 2.5 m and breadth 0.5 m? Given: For the cuboidal shape brick:
length \( (l_1) = 25 \text{ cm}\),
breadth \( (b_1) = 15 \text{ cm}\),
height \( (h_1) = 10 \text{ cm}\)
For the cuboidal shape wall:
length \( (l_2) = 6 \text{ m}\),
height \( (h_2) = 2.5 \text{ m}\),
breadth \( (b_2) = 0.5 \text{ m}\)
To find: Number of bricks required
Solution:
When all the bricks are arranged to build a wall, the volume of all the bricks is equal to volume of wall.
\(\therefore \text{Number of bricks} = \frac{\text{volume of the wall}}{\text{volume of a brick}}\)
(i) Volume of a brick \( = l_1 \times b_1 \times h_1\)
\( = 25 \times 15 \times 10 \text{ cc}\)
(ii) \(l_2 = 6\text{m} = 6 \times 100 \)
\(\implies 1\text{m} = 100\text{cm}\)
\( = 600 \text{ cm}\)
\(h_2 = 2.5 \text{ m} = 2.5 \times 100 = 250 \text{ cm}\)
\(b_2 = 0.5 \text{ m} = 0.5 \times 100 = 50 \text{ cm}\)
Volume of the wall \( = l_2 \times b_2 \times h_2\)
\( = 600 \times 50 \times 250 \text{ cc}\)
(iii) Number of bricks \( = \frac{\text{volume of the wall}}{\text{volume of a brick}}\)
\( = \frac{600 \times 50 \times 250}{25 \times 15 \times 10}\)
\( = 40 \times 2 \times 25\)
\( = 2000 \text{ bricks}\)
\(\therefore 2000 \text{ bricks}\) are required to build the wall.
Answer: \(2000\) bricks are required to build the wall.
In simple words: First, ensure all measurements are in the same unit (centimeters). Then calculate the volume of one brick and the total volume of the wall. The number of bricks needed is the total wall volume divided by the volume of a single brick.

🎯 Exam Tip: Unit consistency is paramount. Convert all measurements to a single unit (e.g., cm) before performing any calculations to avoid errors in the final answer.

Question 4. For rain water harvesting a tank of length 10 m, breadth 6 m and depth 3 m is built. What is the capacity of the tank? How many litre of water can it hold? Given: For a cuboidal tank,
Length \( (l) = 10 \text{ m}\), breadth \( (b) = 6 \text{ m}\), depth \( (h) = 3 \text{ m}\)
To find: Capacity of the tank and litre of water tank can hold.
Solution:
(i) \(l = 10\text{m} = 10 \times 100 \)
\(\implies 1\text{m} = 100\text{cm}\)
\( = 1000 \text{ cm}\),
\(b = 6\text{m} = 6 \times 100 = 600 \text{ cm}\),
\(h = 3\text{m} = 3 \times 100 = 300 \text{ cm}\)
Volume of the tank \( = l \times b \times h\)
\( = 1000 \times 600 \times 300\)
\( = 18,00,00,000 \text{ cc}\)
(ii) Capacity of the tank \( = \text{Volume of the tank}\)
\( = 18,00,00,000 \text{ cc}\)
\( = \frac{18,00,00,000}{1000}\)
\(\therefore 1 \text{ litre} = 1000 \text{ cc}\)
\( = 1,80,000 \text{ litre}\)
\(\therefore\) The capacity of the tank is \(18,00,00,000 \text{ cc}\) and it can hold \(1,80,000 \text{ litre}\) of water.
Answer: The capacity of the tank is \(18,00,00,000 \text{ cc}\) and it can hold \(1,80,000 \text{ litre}\) of water.
In simple words: First, convert all dimensions to centimeters and calculate the volume in cubic centimeters. Then, convert this volume to litres by dividing by 1000, as 1 litre equals 1000 cubic centimeters.

🎯 Exam Tip: Remember the conversion factor: \(1 \text{ litre} = 1000 \text{ cm}^3\). This is crucial for correctly converting volume from cubic centimeters to litres.