- Calculate the following related to square based prisms
a) Volume if the base is 3 cm and ht is 6 cm.
b) Volume if area of base is 20 m2 and ht is 4.5 m
c) Ht if the volume is 490 cm3 and edge is 7 cm.
d) Base if vol is 968 cm3 and ht is 8 cm.
Solution:
(a) A = 3cm , h = 6 cm , volume of square based prism = Bh
V = a2h = 32 x 6 = 9 x 6 = 54 cc
(b) B = 20m2 ; h = 4.5 m; V = ?
V = Bh = 20 x 4.5 = 90m3
(c) V = 490cm3 ; a = 7 cm; h = ?
V = Bh
490 = B x h = a2h
h = 490/7×7 = 10cm
(d) V = 968 cm3 ; h = 8 cm ; a = ?
968 = a2 h = a2 x 8
a2 = 968/8 = 121
a = 11 cm
- Find the volume of a equilateral triangle based prism if the perimeter of the base is 6 cm. and height is 18 cm.
Solution:
Volume equilateral triangle prism = ?
P = 6 cm. ht = 18 cm.
3a = 6
a = 2
Volume of prism = Bh
Base of triangle = √3/4 a2 = √3/4 x2x2 = √3
V = √3×18 = 18√3cm2
- If volume of an equilateral triangle based prism is 72√3 m3 and height is 7 cm. find the base.
Solution:
V = 72√3
h = 7 cm
a = ?
V = Bh
72√3 = B x 7
B = 72√3/7 = 10.28√3m2
B = √3/2 a2
72√3/7 = √3/2 a2
a2 = 72√3/7 x 2/√3
= 72×2/7 = 144/7
- If the volume of square based prism is 250 cm2 and height is 10 cm find TSA.
Solution:
V = 250 = Bh = a2h
h = 10 cm
250 = a2 x 10
a2 = 25
a = 5
TSA = 2B + ph = 2xa2 + 4xaxh
= 2x5x5 + 4x5x10
= 50 + 200
= 250 cm2
- The base of a prism of height 8 cm. is trapezium. If the parallel side area 10 cm. and 16 cm. are at a distance of 8 cm. find the volume.
Solution:
Ht = 8 cm. a = 10 cm. b = 16 cm.
Height between a and b = 8 cm.
Since base is trapezium
Area of trapezium = 1/2 h(a+b)
A = 1/2 x 8 x (10+16)
volume of prism = Bh
= 104 x 8
= 832 cc.
1 thought on “Mensuration – Exercise 4.6.5 – Class IX”
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