Surface Areas and Volumes — Part 1: Surface area of combined solids: visual lesson, CBSE Class 10 Mathematics (Standard 041 / Basic 241)

Lesson

Surface Areas and Volumes, Part 1: Surface area of combined solids

A kulfi is a cone and a hemisphere. What is its surface?

In this lesson you will

Cone (apex down) $+$ hemisphere of the same radius.

Concept

Use the surface-area formulas for cuboid, cube, cylinder, cone, sphere, hemisphere
Find a cone's slant height
Spot the hidden faces when solids are joined
Find surface areas of tents, kulfis, toys and tanks
Handle a hemisphere scooped out of a solid

Diagram

Learn this table: every combined solid is built from it.
Solid	Curved / lateral surface	Total surface	Volume
Cuboid $l \times b \times h$	$2h(l + b)$	$2(lb + bh + hl)$	$lbh$
Cube, edge $a$	$4a^2$	$6a^2$	$a^3$
Cylinder	$2\pi rh$	$2\pi r(r + h)$	$\pi r^2h$
Cone	$\pi rl$	$\pi r(l + r)$	$\dfrac13\pi r^2h$
Sphere	—	$4\pi r^2$	$\dfrac43\pi r^3$
Hemisphere	$2\pi r^2$	$3\pi r^2$	$\dfrac23\pi r^3$

Every combined solid in this chapter is made of two of these.