Question

the volume of a pyramid varies jointly as its height and the area of its base. given that when area of the base is 45.sq. cm, height is 16 cm, the volume is 240 cubic cm. what is the area of base of a pyramid, whose volume is 400 cubic cm and height is 25 cm.​

Answer 1

The volume of a pyramid varies jointly as its height and the area of its base. given that when area of the base is 45.sq. cm, height is 16 cm, the volume is 240 cubic cm. The area of base of a pyramid, whose volume is 400 cubic cm and height is 25 cm is 48 sq.cm

• Given,
• "varies jointly" means V = k*h*b
• where
• k = a constant
• h = height
• b = the area of the base
• 240 = k * 16 * 45
• solving the above equation, we get,
• => k = 1/3
• Therefore
• V = (1/3) * b * h
• 400 = (1/3) * b * 25
• b=400 / [(1/3) * 25]
• => b = 48 sq.cm

Answer 2

Area of base of pyramid is 48 $\mathbf{cm^{2}}$.

Step-by-step explanation:

1. We know that volume of pyramid is directly proportional to  

   product of base area and height of pyramid.

  So

 Volume of pyramid∝ Base area × Height

  ⇒On increasing or decreasing the base area of pyramid will  

      increase or decrease volume of pyramid.

  ⇒On increasing or decreasing the height of pyramid will increase or  

      decrease volume of pyramid.

     So it is case of direct proportion case.

2.

    Base area × Height:-       45×16                                   A×25

     Volume:-                           240                                      400

     Ratio is constant

     Means

     $\mathbf{\frac{A\times 25}{400}=\frac{45\times 16}{240}}$

     $\mathbf{A=\frac{45\times 16}{240}\times \frac{400}{25}}$

     On solving above

     A = 48 $\mathbf{cm^{2}}$ =This is the area of base of a pyramid.