Question

A solid cylinder has diameter 28 cm and height 24 cm. A conical cavity of the same diameter and the same height is drilled out from this solid. Find the whole surface area of the remaining solid.

Answer 1

Answer:

total  surface area of the  solid is  $4564.7 cm^2$

Step-by-step explanation:

Diameter of the cylinder $d = 28 cm$

Height of the cylinder $h = 24 cm$

Surface area of the cylinder lateral surface

$A_{1}= \pi d h\\A_{1}=\pi \times 28 \times 24\\A_{1}=672 \pi cm^2$

When conical cavity is made in solid cylinder, the one of the base will be removed. So we will have only one base area . i,e

$A_{2}=\pi \frac{d^2}{4} \\A_{2}=\pi \frac{28^2}{4}\\A_{2}=196 \pi cm^2$

Surface area of the drilled out cone is

$A_{3}=\pi r(r+\sqrt{r^2+h^2}) \\A_{3}=\pi \times 14(14+\sqrt{14^2+24^2})\\A_{3}=585\pi cm ^2$

total surface area  of the remaining solid is

= Surface area of the cylinder lateral surface+one base area+Surface area of the drilled out cone

$A_{1}+A_{2}+A_{3}\\=672\pi +196\pi +585\pi \\=1453\pi =4564.7 cm^2$

whole surface area of the remaining solid  $4564.7 cm^2$