13. Surface Areas and Volumes Mathematics Exercise - 13.5 class 9 Maths in English - CBSE Study
NCERT Solutions for Class 9 Mathematics are carefully prepared according to the latest CBSE syllabus and NCERT textbooks to help students understand every concept clearly. These solutions cover all important 13. Surface Areas and Volumes with detailed explanations and step-by-step answers for better exam preparation. Each Exercise 13.5 is explained in simple language so that students can easily grasp the fundamentals and improve their academic performance. The study material is designed to support daily homework, revision practice, and final exam preparation for Class 9 students. With accurate answers, concept clarity, and structured content, these NCERT solutions help learners build confidence and score higher marks in their examinations. Whether you are revising a specific topic or preparing an entire chapter, this resource provides reliable and syllabus-based guidance for complete success in Mathematics.
Class 9 English Medium Mathematics All Chapters:
13. Surface Areas and Volumes
5. Exercise 13.5
EXERCISE 13.5
Q1. A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes ?
Solution:
Length = 4 cm, breadth = 2.5 cm, height = 1.5 cm
Volume of cuboid = l × b × h
⇒ 4 × 2.5 × 1.5 cm
⇒ 10 × 1.5
⇒ 15 cm × 3
⇒ 180 cm3
Q2. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000 l)
Solution:
Length = 6 m, width = 5 m, depth = 4.5 m
Volume of cuboid = l × b × h
⇒ 6 × 5 × 4.5 m
⇒ 30 × 4.5
⇒ 135 m3
Water can be hold = 135 × 1000
⇒ 135000 l
Q3. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
Solution:
Length = 10 m, width = 8 m, volume = 380 cm2
Volume of cuboid = l × b × h
380 cm2 = 10 × 8 × h
380 cm2 = 80h
Q4. Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of 30 per m3.
Solution:
Length = 8m, breadth = 6m, height = 3m
Volume of cuboid = l × b × h
⇒ 8 × 6 × 3 m
⇒ 48 × 3 m
⇒ 144 m3
Cost of digging = 144 × 30
⇒ Rs. 4320
Q5. The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
Solution:
1m3 = 1000 l
50000 l = 50 m3
Volume of cuboid = l × b × h
50m3 = 2.5 × 10 × h
50m3 = 25h
Q6. A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
Solution:
Population = 400
Per head per day = 150 l
Total water require per day = 400 × 150
⇒ 600000 Litre
Volume of tank = 20 × 15 × 6 m
⇒ 1800 m3 = 1800000 l
Q7. A godown measures 40 m × 25 m × 15 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.
Solution :
Volume of godown = l × b × h
⇒ 40 × 25 × 15 m
⇒ 15000 m3
Volume of crates = l × b × h
⇒ 1.5 × 1.25 × 0.5 m
⇒ 0.9375 m3
Q8. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Solution:
Volume of cube = a3
⇒ 12 × 12 × 12
⇒ 1728 cm3
Q9. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Solution:
Deep = 3m, width = 40 m, speed = 2 kmph
Volume of river = 2000 × 40 × 3
⇒ 24000 m3
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