Question

a frustum of a pyramid is 6cm square at the bottom 6cm square at the top and 12cm high find the volume of the frustum

Answer 1

◇ Question:

$\textsf{A frustum of a pyramid is 6 cm square at the}$$\textsf{bottom , 6 cm square at the top and 12 cm}$$\textsf{high find the volume of the frustum.}$

◇ Given:

Frustum of a pyramid at the bottom = 6cm²

Frustum of a pyramid at the top = 6cm²

Height of the pyramid = 12 cm

◇ To find:

The volume of the frustum

◇ Taken:

[tex]V=\frac{1}{3}(h)(S1+S2+\sqrt{S1×S2})[/tex]

Where,

V = Volume of the frustum

H = Height

S1 = Area of upper base

S2 = Area of lower base

◇ Solution:

$\bold{V=\frac{1}{3}(12)(6cm+6cm+\sqrt{6cm²×6cm²})}$

$\bold{V=\frac{1}{3}(12)(6cm+6cm+\sqrt{36cm²})}$

$\bold{V=\frac{1}{3}×(12)(6cm+6cm+6cm)}$

$\bold{V=(4)(18cm)}$

$\bold{V=18 cubic\;units ⁴}$

◇ Answer:

So , the volume of the frustum is 18 cubic units ⁴.

◇ Extra information:

$\bold{(i) PT = S×3}$

$\bold{(ii) AT = \frac{H×B}{2}}$

$\bold{Where,}$

(i)PT = Perimeter of the Triangle

S = Length of one side of the triangle

(ii)AT = Area of the triangle

H = Height of the triangle

B = Base of the triangle

HOPE IT HELPS YOU