The volume of two similar solids are 512 cm3&2197cm3 If the smaller solid has a surface are of 960 cm2.?

Question

The volumes of two similar solids are 512 cm3 and 2197 cm3. If the similar solid has a surface area of 960cm2 find the surface area of the larger.

Answer 1

Everything needs to be in the same dimensions, so

(Small Surface Area)^3 (Large Surface Area)^3
-------------------------------- = ---------------------------------------
(Small Volume)^2 (Large Volume)^2

(960)^3 / (512)^2 = x^3 / (2197)^2

3375 = x^3/4826809
x^3 = (3375)(4826809)
x = 2535 cm^2

Answer 2

Given V(l) = 2197 cm3 (volume of the larger)
V(s) = 512 cm3 (volume of the smaller)
S(s) = 960 cm2 (surfece area of the smaller solid)

Required S(l) = ? (surface area of the bigger solid)

Solution 1) By proportion since they are similar solids

S(s) / V(s) = S(l) / V(l)

960 cm2 / 512 cm3 = S(l) / 2197 cm3

By cross multiplication, you will get

512 cm3 S(l) = 960 cm2 x 2197 cm3

512 cm3 S(l) = 2,109,120 cm5

S(l) = 2,109,120 cm5 / 512 cm3

S(l) = 4119.375 or 4, 119 cm2

Solution 2 : By using the relationship between Surface area and Volume

Volume = Surface Area x width (or thickness) of the solid

Vs = Ss x w
512 cm3 = 960 cm2 x w

w = 512 cm3 / 960 cm2
w = 0.5333 cm

Since the two solids are similar, we can assume that they have the same w, such that

Vl = Sl x 0.533333 cm

2197 cm3 = Sl x 0.533333 cm

Sl = 2197 cm3 / 0. 533333 cm

Sl = 4,119.377 or 4,119 cm2 which is similar to the one we got on Solution 1

Answer 3

I'm gonna assume each solid is in the form of a box, so

abc = 512 for smaller.
Call r=ratio, of bigger to smaller, so
r = cuberoot(2197/512) = 1.625 = 13/8

Surface area of smaller =
=2(ab + ac + bc)=960
960*r^2 = 169*960/64 = 169*15 = 2535 cm^2

Answer 4

You don't need to know what their shapes are.
The ratio of volumes is (13/8)^3 therefore the ratio of surface areas is (13/8)^2 so the larger has area 960*(13/8)^2
= 2535cm^2.

Answer 5

V2 = k³.V1 and SA2 = k².SA1
2197 = k³ x 512
k³ = 2197/512 = 4.29
k² = (4.29)^(2/3) = 2.641
Larger surface area = 2.641 x 960 cm² = 2535 cm²

Answer 6

What is the shape of the solid?

Answer 7

I think you better give more details like what kind of solid is it .