A solid wooden toy is prepared by joining a cone, a cylinder and a sphere, as shown in the given diagram. The radius of each of the three solids is 7 cm and heights of each of the cone and the cylinder is 24 cm. Find :
the total surface area of the given solid.
Topic: Mensuration
Answer
Given:
Radius r = 7 cm Height of cone = 24 cm Height of cylinder = 24 cm π = 22/7
First find the slant height of the cone:
l = √(r² + h²)
= √(7² + 24²)
= √(49 + 576)
= √625
= 25 cm
Total surface area of sphere:
= 4πr²
= 4 × 22/7 × 7²
= 616 cm²
Total surface area of cylinder:
= 2πr(h + r)
= 2 × 22/7 × 7 × (24 + 7)
= 1364 cm²
Total surface area of cone:
= πr(r + l)
= 22/7 × 7 × (7 + 25)
= 704 cm²
Required total surface area:
= 616 + 1364 + 704
= 2684 cm²
Answer:
2684 cm².
Find the cone's slant height first using Pythagoras. Then calculate the total surface area of the sphere, cylinder and cone separately and add the three values.