**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 m ^{2} and ht is 4.5 m**

**c) Ht if the volume is 490 cm ^{3} and edge is 7 cm.**

**d) Base if vol is 968 cm ^{3} and ht is 8 cm.**

Solution:

(a) A = 3cm , h = 6 cm , volume of square based prism = Bh

V = a^{2}h = 3^{2} x 6 = 9 x 6 = 54 cc

(b) B = 20m^{2} ; h = 4.5 m; V = ?

V = Bh = 20 x 4.5 = 90m^{3}

(c) V = 490cm^{3} ; a = 7 cm; h = ?

V = Bh

490 = B x h = a^{2}h

h = ^{490}/_{7×7} = 10cm

(d) V = 968 cm^{3} ; h = 8 cm ; a = ?

968 = a^{2} h = a^{2 }x 8

a^{2} = ^{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} a^{2} = ^{√3}/_{4} x2x2 = √3

V = √3×18 = 18√3cm^{2}

**If volume of an equilateral triangle based prism is 72√3 m**^{3}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√3m^{2}

B = ^{√3}/_{2} a^{2}

^{72√3}/_{7} = ^{√3}/_{2} a^{2}

a^{2} = ^{72√3}/_{7} x ^{2}/_{√3}

= ^{72×2}/_{7} = ^{144}/_{7}

**If the volume of square based prism is 250 cm**^{2}and height is 10 cm find TSA.

Solution:

V = 250 = Bh = a^{2}h

h = 10 cm

250 = a^{2} x 10

a^{2} = 25

a = 5

TSA = 2B + ph = 2xa^{2} + 4xaxh

= 2x5x5 + 4x5x10

= 50 + 200

= 250 cm^{2}

**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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