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Surface Areas And Volumes — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsSurface Areas And Volumes3 Marks
Question
Height of a solid cylinder is 10cm and diameter 8cm. Two equal conical hole have been made from its both ends. If the diameter oaf the holes is 6cm and height 4cm, find
  1. volume of the cylinder
  2. volume of one conical hole,
  3. volume of the remaining solid.
✓

Answer

Height = 10cm.
Radius
$=\frac{8}{2}$
$=4\text{cm}$
  1. Volume of cylinder
$=\pi\text{r}^2\text{h}$

$=\pi\times(4)^2\times10$

$=160\pi\ \text{cm}^3$
  1. Volume of conical hole diameter of cone = 6cm.
radius $=\frac{6}{2}$

$=3\text{cm}$

height = 4cm

Volume $=\frac{1}{3}\pi(7)^2\text{h}$

$=\frac{1}{3}\pi.9.4$

$=12\pi\ \text{cm}^3$
  1. Volume of remaining solid
$=160\pi-2\times(12\pi)$

$=160\pi-24\pi$

$=136\pi\ \text{cm}^3$

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