The side of the base of a square pyramid is increasing at a rate of 666 meters per minute and the height of the pyramid is decreasing at a rate of 111 meter per minute. At a certain instant, the base side is 333 meters and the height is 999 meters. What is the rate of change of the volume of the pyramid at that instant (in cubic meters per minute)

Step-by-step explanation:

We are given that

Base side of square pyramid, a=3 m

Height of square pyramid, h=9m

We have to find  the rate of change of the volume of the pyramid at that instant.

Volume of square pyramid, V=

Differentiate w.r.t t

Substitute the values

Hence, the rate of change of the volume of the pyramid at that instant=

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

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