Question

A cake as shown has three layers, each of which is a cuboid. The base of these cuboids are squares whose sides are of length $15cm,30cm$ and $45cm$. The height of each layer is $5cm$. Find the total area of the care that must be frosted. Assume that there will be frosting between the layers, but not at the bottom of the cake.

• A. $5000c{m}^2$
• B. $4000c{m}^2$
• C. $4950c{m}^2$
• D. $4500c{m}^2$

Answer 1

The correct option is C $4950c{m}^2$

Area of the cake to be frosted $=$ Total surface area of all the three layers $-$ Area off bases of all the three layers as they are to be not frosted.
Total surface area of a cuboid $=2(l\times b+b\times h+l\times h)$
$=2(45\times 45+45\times 5+45\times 5)+2(30\times 30+30\times 5+30\times 5)+2(15\times 15+15\times 5+15\times 5)$

$=4950+2400+750=8100{cm}^2$

Area of bases $=45\times 45+30\times 30+15\times 15$

$=2025+900+225=3150{cm}^2$

Area of the cake to be frosted $=8100-3150=4950{cm}^2$