EXERCISE 13.5
Q 1, Ex. 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Page No 228:
Question 1:
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?Answer:
Matchbox is a cuboid having its length (l), breadth (b), height (h) as 4 cm, 2.5 cm, and 1.5 cm.Volume of 1 match box = l × b × h
= (4 × 2.5 × 1.5) cm3 = 15 cm3
Volume of 12 such matchboxes = (15 × 12) cm3
= 180 cm3
Therefore, the volume of 12 match boxes is 180 cm3.
Q 2, Ex. 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 2:
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 = 1000l)Answer:
The given cuboidal water tank has its length (l) as 6 m, breadth (b) as 5 m, and height (h) as 4.5 m.Volume of tank = l × b × h
= (6 × 5 × 4.5) m3 = 135 m3
Amount of water that 1 m3 volume can hold = 1000 litres
Amount of water that 135 m3 volume can hold = (135 × 1000) litres
= 135000 litres
Therefore, such tank can hold up to 135000 litres of water.
Q 3, Ex 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 3:
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?Answer:
Let the height of the cuboidal vessel be h.Length (l) of vessel = 10 m
Width (b) of vessel = 8 m
Volume of vessel = 380 m3
∴ l × b × h = 380
[(10) (8) h] m2= 380 m3
h=4.75m
Therefore, the height of the vessel should be 4.75 m.
Q 4, Ex. 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 4:
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.Answer:
The given cuboidal pit has its length (l) as 8 m, width (b) as 6 m, and depth (h)as 3 m.Volume of pit = l × b × h
= (8 × 6 × 3) m3 = 144 m3
Cost of digging per m3 volume = Rs 30
Cost of digging 144 m3 volume = Rs (144 × 30) = Rs 4320
Q 5, Ex. 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 5:
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.Answer:
Let the breadth of the tank be b m.Length (l) and depth (h) of tank is 2.5 m and 10 m respectively.
Volume of tank = l × b × h
= (2.5 × b × 10) m3
= 25b m3
Capacity of tank = 25b m3 = 25000 b litres
∴ 25000 b = 50000
⇒ b = 2
Therefore, the breadth of the tank is 2 m
Q 6, Ex. 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 6:
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?Answer:
The given tank is cuboidal in shape having its length (l) as 20 m, breadth (b) as 15 m, and height (h) as 6 m.Capacity of tank = l × b× h
= (20 × 15 × 6) m3 = 1800 m3 = 1800000 litres
Water consumed by the people of the village in 1 day = (4000 × 150) litres
= 600000 litres
Let water in this tank last for n days.
Water consumed by all people of village in n days = Capacity of tank
n × 600000 = 1800000
n = 3
Therefore, the water of this tank will last for 3 days.
Q 7, Ex. 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 7:
A godown measures 60 m × 25 m × 10 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.Answer:
The godown has its length (l1) as 60 m, breadth (b1) as 25 m, height (h1) as 10 m, while the wooden crate has its length (l2) as 1.5 m, breadth (b2) as 1.25 m, and height (h2) as 0.5 m.Therefore, volume of godown = l1 × b1 × h1
= (60 × 25 × 10) m3
= 15000 m3
Volume of 1 wooden crate = l2 × b2 × h2
= (1.5 × 1.25 × 0.5) m3
= 0.9375 m3
Let n wooden crates can be stored in the godown.
Therefore, volume of n wooden crates = Volume of godown
0.9375 × n = 15000
n = 150000.9375=16000
Therefore, 16,000 wooden crates can be stored in the godown.
Q 8, Ex. 13.5, Page No 228 , Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 8:
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.Answer:
Side (a) of cube = 12 cmVolume of cube = (a)3 = (12 cm)3 = 1728 cm3
Let the side of the smaller cube be a1.
Volume of 1 smaller cube $=\left(\frac{1728}{8}\right) \mathrm{cm}^{3}$
= 216cm3
$\left(a_{1}\right)^{3}=216 \mathrm{cm}^{3}$
⇒ a1 = 6 cm
Therefore, the side of the smaller cubes will be 6 cm.
Ratio between surface areas of cubes$=\frac{\text { Surface area of bigger cube }}{\text { Surface area of smaller cube }}$
$=\frac{6 a^{2}}{6 a_{1}^{2}}=\frac{(12)^{2}}{(6)^{2}}$
$=\frac{4}{1}$
Therefore, the ratio between the surface areas of these cubes is 4:1
Q 9, Ex. 13.5, Page No 228, Surface Areas & Volumes - NCERT Class 9th Maths Solutions
Question 9:
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?Answer:
Rate of water flow = 2 km per hour$=\left(\frac{2000}{60}\right) \mathrm{m} / \mathrm{min}$
$=\left(\frac{100}{3}\right) \mathrm{m} / \mathrm{min}$
Depth (h) of river = 3 m
Width (b) of river = 40 m
Volume of water flowed in 1 min $=\left(\frac{100}{3} \times 40 \times 3\right) \mathrm{m}^{3}$= 4000 m3
Therefore, in 1 minute, 4000 m3 water will fall in the sea.
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