Question

A wooden doll of height 8 cm is made of with pyramid of slant height 5 cm on its upper part and a prism of base 6×6 cm on its lower part.If all the faces of the doll is paint at the rate of 200 per cm^2 what will be the total cost

Answer 1

The surface area of a three dimensional figure is the sum of the areas of all the faces. To successfully find the total surface area, the following formulae are needed:

Pythagoras Theorem can be applied to missing side of a right angle triangle. Formula for Pythagoras Theorem:  $a^2 + b^2 = c^2$, where c is the hypothenuse.

Also needed in this questions are the formulae for area of triangle and the area of rectangle:

$\text {Area of a triangle } = \dfrac{1}{2} \times \text{base} \times \text{height}$

$\text {Area of the rectangle } = \text{Length } \times \text{Base }$

Given:

Height of the doll = 8 cm

Slanted height = 5 cm

Base Area = 6 cm x 6 cm

Find the height of the pyramid:

$a^2 + b^2 = c^2$

$a^2 + 3^2 = 5^2$

$a^2 = 5^2 - 3^2$

$a^2 = 16$

$a = 4$

Find the height of the prism:

$\text {Height = } 8 - 4$

$\text {Height = } 4 \text{ cm}$

Find the total surface area:

$\text {Area of the 4 triangles } = 4 \times \dfrac{1}{2} \times \text{base} \times \text{height}$

$\text {Area of the 4 triangles } = 4 \times \dfrac{1}{2} \times \text{6} \times \text{5}$

$\text {Area of the 4 triangles } =60 \text { cm}^2$

$\text {Area of the 4 lateral sides of the prism } = 4 \times \text{length} \times \text{height}$

$\text {Area of the 4 lateral sides of the prism } = 4 \times 6 \times 4$

$\text {Area of the 4 lateral sides of the prism } = 96 \text { cm}^2$

$\text {Area of the base } = \text{Length } \times \text{Base }$

$\text {Area of the base } = 6 \times 6$

$\text {Area of the base } = 36 \text { cm}^2$

$\text {Total Surface Area } = 60 + 96 + 36$

$\text {Total Surface Area } = 192 \text { cm}^2$

Find the total cost:

$1 \text{cm}^2 = \text {Rs }200$

$192 \text{cm}^2 = \text {Rs }200 \times 192$

$172 \text{cm}^2 = \text{Rs }38400$

Answer: The total cost is Rs 38400