surface area and volume

Question

Coffee is sold in two different-sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister. Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.

Answer 1

PROBLEM

 

surface area and volume
Coffee is sold in two different-sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister. Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.

 

SOLUTION

 

Volume: V = πr²h

 

Surface Area: SA = 2πr² + 2πrh

 

Radius: r = d/2

 

r_small = (9/2) cm

 

h_small = 12 cm

 

r_large = 9 cm

 

h_large = 24 cm

 

V_small = π(9/2)²(12) = 243π cm³

 

SA_small = 2π(9/2)² + 2π(9/2)(12) = (81/2)π + 108π = (170/2)π cm²

 

V_large = π(9)²(24) = 1944π cm³

SA_large = 2π(9)² + 2π(9)(24) = 162π + 432π = 594π cm²