Mathematics Part ii Solutions Solutions for Class 8 Math Chapter 4 Prisms are provided here with simple step-by-step explanations. These solutions for Prisms are extremely popular among class 8 students for Math Prisms Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Part ii Solutions Book of class 8 Math Chapter 4 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Part ii Solutions Solutions. All Mathematics Part ii Solutions Solutions for class 8 Math are prepared by experts and are 100% accurate.
Page No 127:
Question 1:
Compute the volume and surface area of rectangular prisms of measurements given below:
(i) length 24 centimetres, breadth 15 centimetres, height 32 centimetres
(ii) length 42.5 centimetres, breadth 25 centimetres, height 86 centimetres
(iii) length 37 centimetres, breadth 23 centimetres, height 58 centimetres
Answer:
(i)
Length (l) of the rectangular prism = 24 cm
Breadth (b) of the rectangular prism = 15 cm
Height (h) of the rectangular prism = 32 cm
Volume of the rectangular prism = l × b × h
= 24 cm × 15 cm × 32 cm
= 11520 cm3
Surface area of the rectangular prism = 2(lb + bh + hl)
= 2(24 × 15 + 15 × 32 + 32 × 24) cm2
= 2(360 + 480 + 768) cm2
= 2 × 1608 cm2
= 3216 cm2
(ii)
Length (l) of the rectangular prism = 42.5 cm
Breadth (b) of the rectangular prism = 25 cm
Height (h) of the rectangular prism = 86 cm
Volume of the rectangular prism = l × b × h
= 42.5 cm × 25 cm × 86 cm
= 91375 cm3
Surface area of the rectangular prism = 2(lb + bh + hl)
= 2(42.5 × 25 + 25 × 86 + 86 × 42.5) cm2
= 2(1062.5 + 2150 + 3655) cm2
= 2 × 6867.5 cm2
= 13735 cm2
(iii)
Length (l) of the rectangular prism = 37 cm
Breadth (b) of the rectangular prism = 23 cm
Height (h) of the rectangular prism = 58 cm
Volume of the rectangular prism = l × b × h
= 37 cm × 23 cm × 58 cm
= 49358 cm3
Surface area of the rectangular prism = 2(lb + bh + hl)
= 2(37× 23 + 23 × 58 + 58 × 37) cm2
= 2(851 + 1334 + 2146) cm2
= 2 × 4331 cm2
= 8662 cm2
Page No 127:
Question 2:
The pillars on the veranda of a school are square prisms of base length 20 centimetres and height 2.25 metres. There are 60 such pillars. What is the total cost of painting them all, at 250 rupees per square metre?
Answer:
Each side of the base of the pillar, a = 20 cm = 0.2 m (1 m = 100 cm)
Height of the pillar, h = 2.25 m
Surface area of a square prism = 2a(a + 2h)
∴ Surface area of the pillar = 2 × 0.2 × (0.2 + 2 × 2.25) m2
= 0.4 × (0.2 + 4.5) m2
= 0.4 × 4.7 m2
= 1.88 m2
Surface area of 60 such pillars = 60 × 1.88 m2 = 112.8 m2
Cost of painting per square metre of the pillar = Rs.250
∴ Cost of painting 112.8 m2 area of the pillars = Rs.250 × 112.8 = Rs.28200
Page No 127:
Question 3:
There are two water tanks atop a building, each of height 2 metres. One is a rectangular prism of base lengths 8 metres and 2 metres and the other is a square prism of base length 4 metres. What is the volume of each? What is the cost of painting the outer surface of each tank, at 250 rupees per square metre? Which costs less?
Answer:
Length of the rectangular tank, l = 8 m
Breadth of the rectangular tank, b = 2 m
Height of the rectangular tank, h = 2 m
Each side of the base of the square tank, a = 4 m
Height of the square tank, h = 2 m
Volume of the rectangular tank = l × b × h
= 8 m × 2 m × 2 m
= 32 m3
Volume of the square tank = a × a × h
= 4 m × 4 m × 2 m
= 32 m3
Outer surface area of the rectangular tank = 2(bh + hl)
= 2 (2 × 2 + 2 × 8) m2
= 2(4 + 16) m2
= 2 × 20 m2
= 40 m2
Outer surface area of the square tank = 4ah
= 4 × 4 m × 2 m
= 32 m2
Cost of painting per square metre of the tank = Rs.250
∴ Cost of painting the outer surface area of the rectangular tank = Rs.250 × 40 = Rs.10000
Cost of painting the outer surface area of the square tank = Rs.250 × 32 = Rs.8000
Thus, the painting cost of the square tank is less than the painting cost of the rectangular tank.
Page No 127:
Question 4:
The length, breadth and height of a rectangular prism are 10, 6 and 8 centimetres. Narrow metal strips are to be fixed along all its edges. What is the total length of metal strips needed?
Answer:
Length (l) of the rectangular prism = 10 cm
Breadth (b) of the rectangular prism = 6 cm
Height (h) of the rectangular prism = 8 cm
Surface area of the rectangular prism = 2(lb + bh + hl)
= 2(10 × 6 + 6 × 8 + 8 × 10) cm2
= 2(60 + 48 + 80) cm2
= 2 × 188 cm2
= 376 cm2
Thus, the total length of the metal strips needed to fix along all the edges of the rectangular prism is 376 cm2.
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