Mensuration – Exercise 4.6.5 – Class IX

1. 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

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2. 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

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3. 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

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4. 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

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5. 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.

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