Volume and Surface Area of Geometric Shapes

This article explains how to calculate the volume and surface area of various geometric shapes like cuboid, cylinder, cone, pyramid, prism, etc. with solved examples. It also provides study material, solved assignments, essays, and dissertations on geometry and trigonometry. The article covers topics like calculating the volume and surface area of a pool, square prism, triangular prism, cone, cuboid, triangular pyramid, cylinder, square base pyramid, right rectangle pyramid, and right angle triangular prism.

PART B
Question 4
A.)
Length of pool l = 20 m
Width w = 7 m
Depth h = 1.2 m
Diameter of semicircle = 7
Radius of semicircle = 3.5 m
Area of semi-circle = πr2 / 2
= [ 3.14 * 3.5 * 3.5 ] /2
Area of semi-circle = 19.23 m2
Area of two semi-circles = 2 * 19.23 = 38.6 m2
Lenth of rectangle = 20 – [3.5+3.5] = 13 m
Width of rectangle = 7 m
Area of rectangle = 91 m2
Total surface area of pool = area of rectangle + area of 2 semi-circles
= 91 + 38.6
Total surface area of pool = 129.6 m2
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B.)
Volume of pool = Volume of rectangle + Volume of both semi-circles
Volume of rectangle = length * width * depth
= 13 * 7 * 1.2 = 109.2 m3
Volume of semi-circle = 0.5 * π r2 h
Radius r = 3.5 m
Height h= 1.2 m
Volume = 0.5 * 3.14 * 3.5 *3.5 * 1.2
= 23.07 m3
Volume of pool = 109.2 + 23.07
Volume of pool = 132.27 m3
Question 5
a.)
Square prism
Volume = a2h where a is base edge and h is height
Given h = 15.55 cm and a = 4 cm
Volume = 4 * 4* 15.55
Volume = 248.8 cm3
2

b.)
Triangular prism
Volume = Base area * prism length
Given:
Prism length l = 12 cm
Dimension of base triangle: Base b = 5 cm
Height h = 4.5 cm
Base area = 0.5 * 5 * 4.5 = 11.25
Volume = 11.25 * 12
Volume = 135 cm3
c.)
Cone
3

Volume of cone = [1/3] *π r2 h
Given: diameter d = 15 cm
Radius r = 7.5 cm
Height h = 21 cm
Volume = [1/3] *3.14* 7.5 * 7.5 * 21
Volume = 1236.37 cm3
D.)
Cuboid
Length l = 15 cm
Width w = 7 cm
Height h =3 cm
Volume of cuboid = l * w * h = 15 * 7 *3
Volume = 315 cm3
E.)
4

Triangular pyramid
Volume = [1/3] * base area * height from base to apex
Height from base to apex = h1 = 10 cm
Base area = 0.5 * 7 * 8 = 28 cm
Volume = [1/3] * 28 * 10
Volume = 93.33 cm3
F.)
5

Cylinder
Volume = π r2 h
Diameter d = 8.55 cm
Radius r = 4.27 cm
Height h = 19 cm
Volume = 3.14 * 4.27 * 4.27 * 19
Volume =1087.77 cm3
G.)
Square base pyramid
Volume = [1/3] * Base area * height
Height = 22.50 cm
Length = 12 cm
Width = 9 cm
Base area = 12*9 = 108 cm2
Volume = [1/3] * 108 * 22.50
Volume = 810 cm3
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H.)
Triangular prism
Volume = Base area * prism length
Given:
Prism length l = 10 cm
Dimension of base triangle: Base b = 8 cm
Height h = 3 cm
Base area = 0.5 * 8 * 3 = 12
Volume = 12*10
Volume = 120 cm3
I.)
Right rectangle pyramid
Volume = [l*w*h] / 3
7

Given l = 23.50 cm w = 22 cm h = 28 cm
Volume = [23.50* 22 * 28] / 3
Volume = 4825.33 cm3
J.)
Right angle triangular prism
Volume = Base area * prism length
Given:
Prism length l = 11 cm
Dimension of base triangle: Base b = 4 cm
Height h = 3 cm
Base area = 0.5 * 4* 3 = 6
Volume = 6*11
Volume = 66 cm3
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