the whole surface of a rectangular solid is 448 sq.cm.the length of the solid is twice its breadth and the height is half its breadth.find the volume of the solid
Answers
Answer:
The volume of rectangular solid is 896√14 cubic cm
Step-by-step explanation:
Given as
Area of rectangular solid = A = 448 sq cm
the breadth of solid = b cm
The length of solid = l = 2 b
The height of solid = h =
Let The volume of solid = V cubic cm
According to question
∵ Area = 448 sq cm
Or. l × b = 448
Or, 2 × b × b = 448
Or, b ² =
i..e b² = 224
∴ b = √224
Or, b = 4 √14 cm
So, The breadth = b = 4 √14 cm
The length = 2 × b = 2 × 4 √14 = 8√14 cm
height = = 2√14 cm
Now,
Volume of rectangular solid = l × b × h
Or, V = 8√14 cm × 4√14 cm × 2√14 cm
∴ V = 896√14 cm³
Hence, The volume of rectangular solid is 896√14 cubic cm . Answer
The volume of the solid is 512 cubic. cm.
Step-by-step explanation:
We are given that the whole surface of a rectangular solid is 448 sq.cm.
Also, the length of the solid is twice its breadth and the height is half its breadth.
Let the breadth(B) of solid be cm.
So, the length(L) of the solid will be cm and the height(H) of solid is cm.
Now, the whole surface area of the solid is given by;
2[LB + BH + HL] = 448 sq. cm
2[ ] = 448
So, x = 8 cm which means breadth of the solid is 8 cm.
Length of the solid = cm = 16 cm
Height of the solid = cm = 4 cm
Now, volume of the solid =
= = 512 .