{"id":26251,"date":"2021-06-25T15:34:41","date_gmt":"2021-06-25T10:04:41","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=26251"},"modified":"2021-06-25T15:37:31","modified_gmt":"2021-06-25T10:07:31","slug":"ncert-solutions-for-class-9-maths-chapter-13-ex-13-5","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-13-ex-13-5\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5"},"content":{"rendered":"

These NCERT Solutions for Class 9 Maths<\/a> Chapter 13 Surface Areas and Volumes Ex 13.5 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Exercise 13.5<\/h2>\n

Question 1.
\nA matchbox measure 4 cm \u00d7 2.5 cm \u00d7 1.5 cm. What will be the volume of packets containing 12 such boxes?
\nSolution:
\n\"NCERT
\nWe have given the dimension of match box = 4 cm \u00d7 2.5 cm \u00d7 1.5 cm
\nVolume of matchbox = l \u00d7 b \u00d7 h
\n= 4 \u00d7 2.5 \u00d7 1.5
\n= 15 cm3<\/sup>
\nVolume of 12 such matchbox = 12 \u00d7 15 = 180 cm3<\/sup><\/p>\n

\"NCERT<\/p>\n

Question 2.
\nA cuboidal water tank 6 m long, 5 m, wide, and 4.5 m deep. How many liters of water can it hold? (1 m3<\/sup> = 10001)
\nSolution:
\nWe have given that
\nlength of cuboidal tank = 6m
\n\"NCERT
\nBreadth of cubodical tank = 5 m
\nand height of cubodical tank = 4.5 m
\nVolume of cubodical tank = l \u00d7 b \u00d7 h
\n= 6 \u00d7 5 \u00d7 4.5
\n= 135 m3<\/sup>
\nAgain, we have given that
\n1 m2<\/sup> = 10001
\n135m3<\/sup> = 135 \u00d7 10001 = 1350001
\nTherefore, the cuboidal tank holds 135000 liters of water.<\/p>\n

Question 3.
\nA cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?
\nSolution:
\nWe have given that
\nlength of cuboidal vessel = 10 m
\nBreadth of cuboidal vessel = 8 m
\nand volume of cuboidal vessel = 380 m3<\/sup>
\nWe know that,
\nVolume of cuboidal Vessel = l \u00d7 b \u00d7 h
\n\u21d2 380 = 10 \u00d7 8 \u00d7 h
\n\u21d2 h = 4.75 m
\nTherefore, the height of required cuboidal vessels = 4.75m.<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nFind the cost of digging a cuboidal pit 8m long 6 m broad and 3 m deep at the rate of Rs. 30 per m3<\/sup>.
\nSolution:
\nWe have given that length of cuboidal pit = 8m
\n\"NCERT
\nBreadth of cubodical pit = 6 m
\nand height of cubodical pit = 4 m
\nVolume of cubodical pit = l \u00d7 b \u00d7 h
\n= 8 \u00d7 6 \u00d7 3
\n= 144 m3<\/sup>
\nRate od digging = Rs. 30 per m3<\/sup>
\nTotal cost of digging tire cubodical pit = 30 \u00d7 144 = Rs. 4,320<\/p>\n

Question 5.
\nThe capacity of a cuboidal tank is 50,000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
\nSolution:
\nWe know that
\n1000 liters = 1 m3<\/sup>
\n50,000 liters = 50 m3<\/sup>
\n\"NCERT
\nNow, we have given that length of cuboidal tank = 2.5m
\nand height of cuboidal tank = 10m
\nand volume of cuboidal tank = 50 m3<\/sup>
\nWe know that
\nThe volume of cuboidal tank = l \u00d7 b \u00d7 h
\n\u21d2 50 = 2.5 \u00d7 b \u00d7 10
\n\u21d2 b = 2 m
\nThe breadth of the required tank = 2m.<\/p>\n

\"NCERT<\/p>\n

Question 6.
\nA village, having a population of 4000, requires 1500 liters of water per head per day. It has a tank measuring 20m \u00d7 15m \u00d7 6m. For how many days will the water of this tank last.
\nSolution:
\nVolume of water tank = l \u00d7 b \u00d7 h
\n= 20 \u00d7 15 \u00d7 6
\n= 1800 m3<\/sup>
\n\"NCERT
\nWe know that
\n1 m3<\/sup> = 1000 litres
\n1800 m3<\/sup> = 1800 \u00d7 1000 = 18,00,000 litres
\nTherefore, capacity of water tank = 18,00,000 litres.
\nNow, One person requires 150 litres per day
\n4000 person requires = 4000 \u00d7 150 = 6,00,000 litres per day
\nNo. of days will the water of tank last = \\(\\frac{18,00,000}{6,00,000}\\) = 3 days.<\/p>\n

Question 7.
\nA godown measures 40 m \u00d7 25 m \u00d7 10 m. Find the maximum number of wooden crates each measuring 1.5 m \u00d7 1.25 m \u00d7 0.5 m that can be stored in the godown.
\nSolution:
\nVolume of godown = 40 \u00d7 25 \u00d7 10 = 10,000 m3<\/sup>
\nTherefore, total number of crates can be stored in the godown = \\(\\frac{10,000}{0.9375}\\) = 10666.66 or 10,666.<\/p>\n

Question 8.
\nA 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.
\nSolution:
\nVolume of larger cube = (side)3<\/sup>
\n= (12)3<\/sup>
\n= 1728 cm3<\/sup>
\nNow, volume of each smaller cube = \\(\\frac {1}{8}\\) \u00d7 1728
\n(side)3<\/sup> = 216
\nside = \\(\\sqrt[3]{216}\\) = 6 cm
\nThe side of’new cube = 6 cm
\nAgain, Surface area of larger cube = 6 \u00d7 (side)2<\/sup>
\n= 6 \u00d7 (12)2<\/sup>
\n= 864 cm2<\/sup>
\nand surface area of smaller cube = 6 \u00d7 (side)2<\/sup>
\n= 6 \u00d7 (6)2<\/sup>
\n= 216 cm2<\/sup>
\nRatio between them is = 984 : 216 = 4 : 1<\/p>\n

\"NCERT<\/p>\n

Question 9.
\nA 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 min?
\nSolution:
\n\"NCERT
\nWe have given that
\nRate of flowing = 2 km\/h 100 m
\n= \\(\\frac{2 \\times 1000}{60}\\) m\/min
\n= \\(\\frac{100}{3}\\) m\/min.
\n\u2234 Volume of water will fall into the sea in one min is = 40 \u00d7 3 \u00d7 \\(\\frac{100}{3}\\) = 4,000 m3<\/sup>.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Exercise 13.5 Question 1. A matchbox measure 4 cm \u00d7 2.5 cm \u00d7 1.5 cm. What will …<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-13-ex-13-5\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 Questions and Answers are prepared by our highly skilled subject experts. 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